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Sample records for ginzburg-landau equation solved

  1. Breaking the hidden symmetry in the Ginzburg-Landau equation

    NARCIS (Netherlands)

    Doelman, A.

    1997-01-01

    In this paper we study localised, traveling, solutions to a Ginzburg-Landau equation to which we have added a small, O ( " ), 0 < "? 1, quintic term. We consider this term as a model for the higher order nonlinearities which appear in the derivation of the Ginzburg-Landau equation. By a combination

  2. Breaking the hidden symmetry in the Ginzburg-Landau equation

    NARCIS (Netherlands)

    Doelman, A.

    1996-01-01

    In this paper we study localised, traveling, solutions to a Ginzburg-Landau equation to which we have added a small, O(e), 0 < e << 1, quintic term. We consider this term as a model for the higher order nonlinearities which appear in the derivation of the Ginzburg-Landau equation. By a combination

  3. Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation

    Energy Technology Data Exchange (ETDEWEB)

    Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel

    2009-06-15

    A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)

  4. Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation

    International Nuclear Information System (INIS)

    Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel

    2009-01-01

    A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)

  5. Exact solutions of generalized Zakharov and Ginzburg-Landau equations

    International Nuclear Information System (INIS)

    Zhang Jinliang; Wang Mingliang; Gao Kequan

    2007-01-01

    By using the homogeneous balance principle, the exact solutions of the generalized Zakharov equations and generalized Ginzburg-Landau equation are obtained with the aid of a set of subsidiary higher-order ordinary differential equations (sub-equations for short)

  6. Numerical Analysis of Ginzburg-Landau Models for Superconductivity.

    Science.gov (United States)

    Coskun, Erhan

    Thin film conventional, as well as High T _{c} superconductors of various geometric shapes placed under both uniform and variable strength magnetic field are studied using the universially accepted macroscopic Ginzburg-Landau model. A series of new theoretical results concerning the properties of solution is presented using the semi -discrete time-dependent Ginzburg-Landau equations, staggered grid setup and natural boundary conditions. Efficient serial algorithms including a novel adaptive algorithm is developed and successfully implemented for solving the governing highly nonlinear parabolic system of equations. Refinement technique used in the adaptive algorithm is based on modified forward Euler method which was also developed by us to ease the restriction on time step size for stability considerations. Stability and convergence properties of forward and modified forward Euler schemes are studied. Numerical simulations of various recent physical experiments of technological importance such as vortes motion and pinning are performed. The numerical code for solving time-dependent Ginzburg-Landau equations is parallelized using BlockComm -Chameleon and PCN. The parallel code was run on the distributed memory multiprocessors intel iPSC/860, IBM-SP1 and cluster of Sun Sparc workstations, all located at Mathematics and Computer Science Division, Argonne National Laboratory.

  7. Integrability and structural stability of solutions to the Ginzburg-Landau equation

    Science.gov (United States)

    Keefe, Laurence R.

    1986-01-01

    The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

  8. Ginzburg-Landau equation as a heuristic model for generating rogue waves

    Science.gov (United States)

    Lechuga, Antonio

    2016-04-01

    Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.

  9. Drift of Spiral Waves in Complex Ginzburg-Landau Equation

    International Nuclear Information System (INIS)

    Yang Junzhong; Zhang Mei

    2006-01-01

    The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg-Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.

  10. Ginzburg-Landau equation and vortex liquid phase of Fermi liquid superconductors

    International Nuclear Information System (INIS)

    Ng, T-K; Tse, W-T

    2007-01-01

    In this paper we study the Ginzburg-Landau (GL) equation for Fermi liquid superconductors with strong Landau interactions F 0s and F 1s . We show that Landau interactions renormalize two parameters entering the GL equation, leading to the renormalization of the compressibility and superfluid density. The renormalization of the superfluid density in turn leads to an unconventional (2D) Berezinskii-Kosterlitz-Thouless (BKT) transition and vortex liquid phase. Application of the GL equation to describe underdoped high-T c cuprates is discussed

  11. Gauges for the Ginzburg-Landau equations of superconductivity

    International Nuclear Information System (INIS)

    Fleckinger-Pelle, J.; Kaper, H.G.

    1995-01-01

    This note is concerned with gauge choices for the time-dependent Ginzburg-Landau equations of superconductivity. The requiations model the state of a superconducting sample in a magnetic field near the critical tempeature. Any two solutions related through a ''gauge transformation'' describe the same state and are physically indistinquishable. This ''gauge invariance'' can be exploited for analtyical and numerical purposes. A new gauge is proposed, which reduces the equations to a particularly attractive form

  12. Ginzburg-Landau-type theory of nonpolarized spin superconductivity

    Science.gov (United States)

    Lv, Peng; Bao, Zhi-qiang; Guo, Ai-Min; Xie, X. C.; Sun, Qing-Feng

    2017-01-01

    Since the concept of spin superconductor was proposed, all the related studies concentrate on the spin-polarized case. Here, we generalize the study to the spin-non-polarized case. The free energy of nonpolarized spin superconductor is obtained, and Ginzburg-Landau-type equations are derived by using the variational method. These Ginzburg-Landau-type equations can be reduced to the spin-polarized case when the spin direction is fixed. Moreover, the expressions of super linear and angular spin currents inside the superconductor are derived. We demonstrate that the electric field induced by the super spin current is equal to the one induced by an equivalent charge obtained from the second Ginzburg-Landau-type equation, which shows self-consistency of our theory. By applying these Ginzburg-Landau-type equations, the effect of electric field on the superconductor is also studied. These results will help us get a better understanding of the spin superconductor and related topics such as the Bose-Einstein condensate of magnons and spin superfluidity.

  13. Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel; Kofane, Timoleon Crepin

    2003-01-01

    The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

  14. ABOUT SOME APPROXIMATIONS TO THE CLOSED SET OF NOT TRIVIAL SOLUTIONS OF THE EQUATIONS OF GINZBURG - LANDAU

    Directory of Open Access Journals (Sweden)

    A. A. Fonarev

    2014-01-01

    Full Text Available Possibility of use of a projective iterative method for search of approximations to the closed set of not trivial generalised solutions of a boundary value problem for Ginzburg - Landau's equations of the phenomenological theory of superconduction is investigated. The projective iterative method combines a projective method and iterative process. The generalised solutions of a boundary value problem for Ginzburg - Landau's equations are critical points of a functional of a superconductor free energy.

  15. Efficient solution of 3D Ginzburg-Landau problem for mesoscopic superconductors

    International Nuclear Information System (INIS)

    Pereira, Paulo J; Moshchalkov, Victor V; Chibotaru, Liviu F

    2014-01-01

    The recently proposed approach for the solution of Ginzburg-Landau (GL) problem for 2D samples of arbitrary shape is, in this article, extended over 3D samples having the shape of (i) a prism with arbitrary base and (ii) a solid of revolution with arbitrary profile. Starting from the set of Laplace operator eigenfunctions of a 2D object, we construct an approximation to or the exact eigenfunctions of the Laplace operator of a 3D structure by applying an extrusion or revolution to these solutions. This set of functions is used as the basis to construct the solutions of the linearized GL equation. These solutions are then used as basis for the non-linear GL equation much like the famous LCAO method. To solve the non-linear equation, we used the Newton-Raphson method starting from the solution of the linear equation, i.e., the nucleation distribution of superconducting condensate. The vector potential approximations typically used in 2D cases, i.e., considering it as corresponding to applied constant field, are in the 3D case harder to justify. For that reason, we use a locally corrected Nystrom method to solve the second Ginzburg-Landau equation. The complete solution of GL problem is then achieved by solving self-consistently both equations

  16. Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation

    International Nuclear Information System (INIS)

    Keefe, L.R.

    1984-01-01

    The bifurcation structure of even, spatially periodic solutions to the time-dependent Ginzburg-Landau equation is investigated analytically and numerically. A rich variety of behavior, including limit cycles, two-tori, period-doubling sequences, and strange attractors are found to exist in the phase space of the solutions constructed from spatial Fourier modes. Beginning with unstable perturbations to the spatially homogeneous Stokes solution, changes in solution behavior are examined as the perturbing wavenumber q is varied in the range 0.6 to 1.3. Solution bifurcations as q changes are often found to be associated with symmetry making or breaking changes in the structure of attractors in phase space. Two distinct mirror image attractors are found to coexist for many values of q. Chaotic motion is found for two ranges of q Lyapunov exponents of the solutions and the Lyapunov dimension of the corresponding attractors are calculated for the larger of these regions. Poincare sections of the attractors within this chaotic range are consistent with the dimension calculation and also reveal a bifurcation structure within the chaos which broadly resembles that found in one-dimensional quadratic maps. The integrability of the Ginzburg-Landau equation is also examined. It is demonstrated that the equation does not possess the Painleve property, except for a special case of the coefficients which corresponds to the integrable non-linear Schroedinger (NLS) equation

  17. Spectrum of the linearized operator for the Ginzburg-Landau equation

    Directory of Open Access Journals (Sweden)

    Tai-Chia Lin

    2000-06-01

    Full Text Available We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.

  18. Variational principles for Ginzburg-Landau equation by He's semi-inverse method

    International Nuclear Information System (INIS)

    Liu, W.Y.; Yu, Y.J.; Chen, L.D.

    2007-01-01

    Via the semi-inverse method of establishing variational principles proposed by He, a generalized variational principle is established for Ginzburg-Landau equation. The present theory provides a quite straightforward tool to the search for various variational principles for physical problems. This paper aims at providing a more complete theoretical basis for applications using finite element and other direct variational methods

  19. Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method

    Energy Technology Data Exchange (ETDEWEB)

    Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)

    2010-04-15

    Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)

  20. Noise-sustained structure, Intermittency, and the Ginzburg--Landau equation

    International Nuclear Information System (INIS)

    Deissler, R.J.

    1985-01-01

    The time-dependent generalized Ginzburg--Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in the stationary frame of refernce and with nonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that the microscopic noise plays an importuant role in the macroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested

  1. Pattern selection and spatio-temporal transition to chaos in Ginzburg-Landau equation

    Energy Technology Data Exchange (ETDEWEB)

    Nozaki, K; Bekki, N

    1983-07-01

    It is shown that a modulationally unstable pattern is selected and propagates into an initially unstable motionless state in the 1-D generalized Ginzburg-Landau equation. A further spatio-temporal transition occurs with a sharp interface from the selected unstable pattern to a stabilized pattern or a chaotic state. The distinct transition makes a coherent structure to coexist with a chaotic state. 12 refs., 4 figs.

  2. Landau-Ginzburg skeletons

    Energy Technology Data Exchange (ETDEWEB)

    Davenport, Ian C.; Melnikov, Ilarion V. [Department of Physics and Astronomy, James Madison University,Harrisonburg, VA 22807 (United States)

    2017-05-10

    We study the class of indecomposable two-dimensional Landau-Ginzburg theories with (2,2) supersymmetry and central charge c < 6 with the aim of classifying all such theories up to marginal deformations. Our results include cases overlooked in previous classifications. The results are rigorous for three or fewer fields and more generally are rigorous if we assume an extra bound. Numerics suggest that we have the complete set of indecomposable Landau-Ginzburg families with c < 6. This set consists of 38 infinite families and a finite list of 418 sporadic cases. The basic tools are classic results of Kreuzer and Skarke on quasi-homogeneous isolated singularities and solutions to certain feasibility integer programming problems.

  3. Time-dependent Ginzburg-Landau equations for rotating and accelerating superconductors

    Czech Academy of Sciences Publication Activity Database

    Lipavský, P.; Bok, J.; Koláček, Jan

    2013-01-01

    Roč. 492, Sept (2013), 144-151 ISSN 0921-4534 R&D Projects: GA ČR(CZ) GAP204/11/0015 Institutional support: RVO:68378271 Keywords : superconductivity * Ginzburg-Landau theory * London field Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.110, year: 2013

  4. Plain and oscillatory solitons of the cubic complex Ginzburg-Landau equation with nonlinear gradient terms

    Science.gov (United States)

    Facão, M.; Carvalho, M. I.

    2017-10-01

    In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrödinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.

  5. Chiral algebras in Landau-Ginzburg models

    Science.gov (United States)

    Dedushenko, Mykola

    2018-03-01

    Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.

  6. Ultrashort optical solitons in the cubic-quintic complex Ginzburg-Landau equation with higher-order terms

    International Nuclear Information System (INIS)

    Fewo, Serge I.; Kofane, Timoleon C.; Ngabireng, Claude M.

    2008-01-01

    With the help of the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fiber is derived, namely the higher-order complex Ginzburg-Landau equation (HCGLE). Considering this one-dimensional HCGLE, we obtain a set of differential equations characterizing the variation of the pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to observe the behaviour of pulse parameters along the optical fiber. A fully numerical simulation of the one-dimensional HCGLE finally tests the results of the CV theory. A good agreement between both methods is observed. Among various behaviours, chaotic pulses, attenuate pulses and stable pulses can be obtained under certain parameter values. (author)

  7. Ginzburg-Landau equations for a d-wave superconductor with applications to vortex structure and surface problems

    International Nuclear Information System (INIS)

    Xu, J.; Ren, Y.; Ting, C.S.

    1995-01-01

    The properties of a d x 2 -y 2 -wave superconductor in an external magnetic field are investigated on the basis of Gorkov's theory of weakly coupled superconductors. The Ginzburg-Landau (GL) equations, which govern the spatial variations of the order parameter and the supercurrent, are microscopically derived. The single vortex structure and surface problems in such a superconductor are studied using these equations. It is shown that the d-wave vortex structure is very different from the conventional s-wave vortex: the s-wave and d-wave components, with the opposite winding numbers, are found to coexist in the region near the vortex core. The supercurrent and local magnetic field around the vortex are calculated. Far away from the vortex core, both of them exhibit a fourfold symmetry, in contrast to an s-wave superconductor. The surface problem in a d-wave superconductor is also studied by solving the GL equations. The total order parameter near the surface is always a real combination of s- and d-wave components, which means that the proximity effect cannot induce a time-reversal symmetry-breaking state at the surface

  8. Solution Theory of Ginzburg-Landau Theory on BCS-BEC Crossover

    Directory of Open Access Journals (Sweden)

    Shuhong Chen

    2014-01-01

    Full Text Available We establish strong solution theory of time-dependent Ginzburg-Landau (TDGL systems on BCS-BEC crossover. By the properties of Besov, Sobolev spaces, and Fourier functions and the method of bootstrapping argument, we deduce that the global existence of strong solutions to time-dependent Ginzburg-Landau systems on BCS-BEC crossover in various spatial dimensions.

  9. Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

    Science.gov (United States)

    Mohebbi, Akbar

    2018-02-01

    In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

  10. Ginzburg-Landau vortices

    CERN Document Server

    Bethuel, Fabrice; Helein, Frederic

    2017-01-01

    This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small.  Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The singularities have infinite energy, but after removing the core energy we are lead to a concept of finite renormalized energy.  The location of the singularities is completely determined by minimiz...

  11. Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

    OpenAIRE

    Berglund, P.; Henningson, M.

    1994-01-01

    We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirr...

  12. Geometric singularities and spectra of Landau-Ginzburg models

    International Nuclear Information System (INIS)

    Greene, B.R.; Roan, S.S.; Yau, S.T.

    1991-01-01

    Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginsburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complementary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance of unorbifolded Landau-Ginzburg theories. (orig.)

  13. Domain Walls and Textured Vortices in a Two-Component Ginzburg-Landau Model

    DEFF Research Database (Denmark)

    Madsen, Søren Peder; Gaididei, Yu. B.; Christiansen, Peter Leth

    2005-01-01

    coupling between the two order parameters a ''textured vortex'' is found by analytical and numerical solution of the Ginzburg-Landau equations. With a Josephson type coupling between the two order parameters we find the system to split up in two domains separated by a domain wall, where the order parameter...... is depressed to zero....

  14. About Ginzburg-Landau, and a bit on others

    International Nuclear Information System (INIS)

    Maksimov, Evgenii G

    2011-01-01

    This note is a brief history of how the theory of Ginzburg and Landau came to be. Early publications on the macroscopic theory of superconductivity are reviewed in detail. Discussions that the two co-authors had with their colleagues and between themselves are described. The 1952 review by V L Ginzburg is discussed, in which a number of well-defined requirements on the yet-to-be-developed microscopic theory of superconductivity were formulated, constituting what J Bardeen called the 'Ginzburg energy gap model'. (from the history of physics)

  15. Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

    Science.gov (United States)

    Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

    2016-11-01

    Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

  16. Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains II: The monotone case

    Science.gov (United States)

    Zhou, Feng; Sun, Chunyou; Cheng, Jiaqi

    2018-02-01

    In this article, we continue the study of the dynamics of the following complex Ginzburg-Landau equation ∂tu - (λ + iα)Δu + (κ + iβ)|u|p-2u - γu = f(t) on non-cylindrical domains. We assume that the spatial domains are bounded and increase with time, which is different from the diffeomorphism case presented in Zhou and Sun [Discrete Contin. Dyn. Syst., Ser. B 21, 3767-3792 (2016)]. We develop a new penalty function to establish the existence and uniqueness of a variational solution satisfying energy equality as well as some energy inequalities and prove the existence of a D -pullback attractor for the non-autonomous dynamical system generated by this class of solutions.

  17. The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation

    KAUST Repository

    Aguareles, M.

    2014-01-01

    In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d

  18. Microscopic Derivation of the Ginzburg-Landau Model

    DEFF Research Database (Denmark)

    Frank, Rupert; Hainzl, Christian; Seiringer, Robert

    2014-01-01

    We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit...

  19. Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors

    Science.gov (United States)

    Liarte, Danilo B.; Transtrum, Mark K.; Sethna, James P.

    2016-10-01

    We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for κ =λ /ξ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB2 suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter κ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and κ , showing type I, type II, or mixed behavior (within Ginzburg-Landau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.

  20. A collective variable approach and stabilization for dispersion-managed optical solitons in the quintic complex Ginzburg-Landau equation as perturbations of the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C

    2006-01-01

    With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods

  1. Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent

    CERN Document Server

    Dvali, Gia

    2012-01-01

    Recently we have suggested that the microscopic quantum description of a black hole is an overpacked self-sustained Bose-condensate of N weakly-interacting soft gravitons, which obeys the rules of 't Hooft's large-N physics. In this note we derive an effective Landau-Ginzburg Lagrangian for the condensate and show that it becomes an exact description in a semi-classical limit that serves as the black hole analog of 't Hooft's planar limit. The role of a weakly-coupled Landau-Ginzburg order parameter is played by N. This description consistently reproduces the known properties of black holes in semi-classical limit. Hawking radiation, as the quantum depletion of the condensate, is described by the slow-roll of the field N. In the semiclassical limit, where black holes of arbitrarily small size are allowed, the equation of depletion is self similar leading to a scaling law for the black hole size with critical exponent 1/3.

  2. Irreducible diagrams in Landau-Ginzburg field theory

    Energy Technology Data Exchange (ETDEWEB)

    Witten, Jr, T A [Michigan Univ., Ann Arbor (USA). Dept. of Psychology

    1981-10-19

    It is shown that the free energy W of a Landau-Ginzburg-Wilson field theory with O(n) symmetry may be written in terms of the generating function V of diagrams irreducible in both propagator and interaction lines. This generalizes and simplifies a recent result of Des Cloizeaux. The functions W and V are related by a type of Legendre transformation on the bare mass variable.

  3. On the Ginzburg-Landau critical field in three dimensions

    DEFF Research Database (Denmark)

    Fournais, Søren; Helffer, Bernard

    2009-01-01

    We study the three-dimensional Ginzburg-Landau model of superconductivity. Several natural definitions of the (third) critical field, HC3, governing the transition from the superconducting state to the normal state, are considered. We analyze the relation between these fields and give conditions ...

  4. Fractional generalization of the Ginzburg–Landau equation: an unconventional approach to critical phenomena in complex media

    DEFF Research Database (Denmark)

    Milovanov, A.V.; Juul Rasmussen, J.

    2005-01-01

    Equations built on fractional derivatives prove to be a powerful tool in the description of complex systems when the effects of singularity, fractal supports, and long-range dependence play a role. In this Letter, we advocate an application of the fractional derivative formalism to a fairly general...... class of critical phenomena when the organization of the system near the phase transition point is influenced by a competing nonlocal ordering. Fractional modifications of the free energy functional at criticality and of the widely known Ginzburg-Landau equation central to the classical Landau theory...... of second-type phase transitions are discussed in some detail. An implication of the fractional Ginzburg-Landau equation is a renormalization of the transition temperature owing to the nonlocality present. (c) 2005 Elsevier B.V. All rights reserved....

  5. Boundary condition for Ginzburg-Landau theory of superconducting layers

    Czech Academy of Sciences Publication Activity Database

    Koláček, Jan; Lipavský, Pavel; Morawetz, K.; Brandt, E. H.

    2009-01-01

    Roč. 79, č. 17 (2009), 174510/1-174510/6 ISSN 1098-0121 R&D Projects: GA ČR GA202/08/0326; GA AV ČR IAA100100712 Institutional research plan: CEZ:AV0Z10100521 Keywords : superconductivity * Ginzburg-Landau theory Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.475, year: 2009

  6. Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

    DEFF Research Database (Denmark)

    Kachmar, Ayman

    2010-01-01

    This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied ...

  7. Disordered λ φ4+ρ φ6 Landau-Ginzburg model

    Science.gov (United States)

    Diaz, R. Acosta; Svaiter, N. F.; Krein, G.; Zarro, C. A. D.

    2018-03-01

    We discuss a disordered λ φ4+ρ φ6 Landau-Ginzburg model defined in a d -dimensional space. First we adopt the standard procedure of averaging the disorder-dependent free energy of the model. The dominant contribution to this quantity is represented by a series of the replica partition functions of the system. Next, using the replica-symmetry ansatz in the saddle-point equations, we prove that the average free energy represents a system with multiple ground states with different order parameters. For low temperatures we show the presence of metastable equilibrium states for some replica fields for a range of values of the physical parameters. Finally, going beyond the mean-field approximation, the one-loop renormalization of this model is performed, in the leading-order replica partition function.

  8. Theory of a condensed charged-Bose, charged Fermi gas and Ginzburg--Landau studies of superfluid 3He

    International Nuclear Information System (INIS)

    Dahl, D.A.

    1976-01-01

    Two independent topics in the field of condensed matter physics are examined: the condensed charged-Bose, charged Fermi gas and superfluid 3 He. Green's function (field theoretic) methods are used to derive the low-temperature properties of a dense, neutral gas of condensed charged bosons and degenerate charged fermions. Restriction is made to the case where the fermion mass is much lighter than the boson mass. Linear response and the density-density correlation function are examined and shown to exhibit two collective modes: a plasmon branch and a phonon branch with speed equal to that of ionic sound in solids. Comparison with a possible astrophysical application (white dwarf stars) is made. The behavior near the superfluid transition temperature (Ginzburg--Landau regime) of 3 He is then studied. Gorkov equations are derived and studied in the weak-coupling limit. In this way the form and order of magnitude estimates of coefficients appearing in the Ginzburg--Landau theory are obtained. Weak-coupling particle and spin currents are derived. Various perturbations break the large degeneracy of the states and have experimental implications. The electric contribution to the Ginzburg--Landau free energy is studied for the proposed A and B phases. Imposition of an electric field orients the axial state, but does not give rise to shifts in the NMR resonances. Shifts and discontinuous jumps in the longitudinal and transverse signals are predicted for the Balian--Werthamer state, the details depending on the relative strengths of the fields, as well as the angle between them

  9. Self-consistent Ginzburg-Landau theory for transport currents in superconductors

    DEFF Research Database (Denmark)

    Ögren, Magnus; Sørensen, Mads Peter; Pedersen, Niels Falsig

    2012-01-01

    We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in princi...... in principle also be used for general geometries in three-dimensional superconductors....

  10. The cubic-quintic-septic complex Ginzburg-Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

    Science.gov (United States)

    Djoko, Martin; Kofane, T. C.

    2018-06-01

    We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

  11. Electrostatic field in superconductors IV: theory of Ginzburg-Landau type

    Czech Academy of Sciences Publication Activity Database

    Lipavský, Pavel; Koláček, Jan

    2009-01-01

    Roč. 23, 20-21 (2009), s. 4505-4511 ISSN 0217-9792 R&D Projects: GA ČR GA202/04/0585; GA ČR GA202/05/0173; GA AV ČR IAA1010312 Institutional research plan: CEZ:AV0Z10100521 Keywords : superconductivity * Ginzburg-Landau theory Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.408, year: 2009

  12. Periods for Calabi-Yau and Landau-Ginzburg vacua

    CERN Document Server

    Berglund, P; De la Ossa, X C; Font, A; Hübsch, T; Jancic, D; Quevedo, Fernando; Berglund, Per; Candelas, Philip; Ossa, Xenia de la; Font, Anamaria; Hubsch, Tristan; Jancic, Dubravka; Quevedo, Fernando

    1994-01-01

    The complete structure of the moduli space of \\cys\\ and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of \\cys. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.

  13. Statistical mechanics of low-dimensional Ginzburg-Landau fields. Some new results

    International Nuclear Information System (INIS)

    Barsan, V.

    1987-08-01

    The Ginzburg-Landau theory for low-dimensional systems is approached using the transfer matrix method. Analitical formulae for the thermodynamical quantities of interest are obtained in the one-dimensional case. An exact expression for the free energy of of a planar array of linear chains is deduced. A good agrement with numerical and experimental data is found.(authors)

  14. Geometry of (0,2) Landau-Ginzburg orbifolds

    International Nuclear Information System (INIS)

    Kawai, Toshiya; Mohri, Kenji

    1994-01-01

    Several aspects of (0,2) Landau-Ginzburg orbifolds are investigated. Especially the elliptic genera are computed in general and, for a class of models recently invented by Distler and Kachru, they are compared with the ones from (0,2) sigma models. Our formalism gives an easy way to calculate the generation numbers for lots of Distler-Kachru models even if they are based on singular Calabi-Yau spaces. We also make some general remarks on the Born-Oppenheimer calculation of the ground states elucidating its mathematical meaning in the untwisted sector. For Distler-Kachru models based on non-singular Calabi-Yau spaces we show that there exist ''residue'' type formulas of the elliptic genera as well. ((orig.))

  15. Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction

    DEFF Research Database (Denmark)

    Frank, Rupert; Hanizl, Christian; Seiringer, Robert

    2013-01-01

    In a recent paper we give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Here we present our results in the simplified case of a one-dimensional system of particles interacting via a delta-potential....

  16. Gradient corrections to the time-dependent Ginzburg-Landau eqzation for anisotropic perturbations of quasiparticles

    Czech Academy of Sciences Publication Activity Database

    Lin, P.-J.; Lipavský, Pavel

    2008-01-01

    Roč. 77, č. 14 (2008), 144505/1-144505/16 ISSN 1098-0121 Institutional research plan: CEZ:AV0Z10100521 Keywords : non-equilibrium superconductivity * Ginzburg-Landau theory Subject RIV: BE - Theoretical Physics Impact factor: 3.322, year: 2008

  17. Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy

    International Nuclear Information System (INIS)

    Aoyama, S.; Kodama, Y.

    1996-01-01

    Based on the dispersionless KP (dKP) theory, we study a topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form treating all the primaries in an equal basis, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having a finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formula for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space. (orig.)

  18. Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

    Science.gov (United States)

    Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

    2017-10-01

    In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

  19. Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents

    International Nuclear Information System (INIS)

    Rubinstein, J.

    1996-01-01

    Our objective is to explain the phenomenon of permanent currents within the context of the Ginzburg-Landau model for superconductors. Using variational techniques we make a connection between the formation of permanent currents and the topology of the superconducting sample. (orig.)

  20. An Approach to Quad Meshing Based On Cross Valued Maps and the Ginzburg-Landau Theory

    Energy Technology Data Exchange (ETDEWEB)

    Viertel, Ryan [Univ. of Utah, Salt Lake City, UT (United States). Dept. of Mathematics; Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Osting, Braxton [Univ. of Utah, Salt Lake City, UT (United States). Dept. of Mathematics

    2017-08-01

    A generalization of vector fields, referred to as N-direction fields or cross fields when N=4, has been recently introduced and studied for geometry processing, with applications in quadrilateral (quad) meshing, texture mapping, and parameterization. We make the observation that cross field design for two-dimensional quad meshing is related to the well-known Ginzburg-Landau problem from mathematical physics. This identification yields a variety of theoretical tools for efficiently computing boundary-aligned quad meshes, with provable guarantees on the resulting mesh, for example, the number of mesh defects and bounds on the defect locations. The procedure for generating the quad mesh is to (i) find a complex-valued "representation" field that minimizes the Dirichlet energy subject to a boundary constraint, (ii) convert the representation field into a boundary-aligned, smooth cross field, (iii) use separatrices of the cross field to partition the domain into four sided regions, and (iv) mesh each of these four-sided regions using standard techniques. Under certain assumptions on the geometry of the domain, we prove that this procedure can be used to produce a cross field whose separatrices partition the domain into four sided regions. To solve the energy minimization problem for the representation field, we use an extension of the Merriman-Bence-Osher (MBO) threshold dynamics method, originally conceived as an algorithm to simulate motion by mean curvature, to minimize the Ginzburg-Landau energy for the optimal representation field. Lastly, we demonstrate the method on a variety of test domains.

  1. Construction of the dual Ginzburg-Landau theory from the lattice QCD

    International Nuclear Information System (INIS)

    Suganuma, H.; Amemiya, K.; Ichie, H.; Koma, Y.

    2002-01-01

    We roughly review the QCD physics and then introduce recent topics on the confinement physics. In the maximally abelian (MA) gauge, the low-energy QCD is abelianized owing to the effective off-diagonal gluon mass M off ≅ 1.2 GeV induced by the MA gauge fixing. We demonstrate the construction of the dual Ginzburg-Landau (DGL) theory from the low-energy QCD in the MA gauge in terms of the lattice QCD evidences on infrared abelian dominance and infrared monopole condensation. (author)

  2. Specific heat of Ginzburg-Landau fields in the n-1 expansion

    International Nuclear Information System (INIS)

    Bray, A.J.

    1975-01-01

    The n -1 expansion for the specific heat C/subv/ of the n-component Ginzburg-Landau model is discussed in terms of an n -1 expansion for the irreducible polarization. In the low-temperature limit, each successive term of the latter expansion diverges more strongly than the last, invalidating a truncation of this series at any finite order in 1/n. The most divergent terms in each order are identified and summed. The results provide justification for the usual truncated expansions for C/subv/

  3. Dual Ginzburg-Landau theory and quark nuclear physics

    International Nuclear Information System (INIS)

    Toki, H.; Suganuma, H.; Ichie, H.; Monden, H.; Umisedo, S.

    1998-01-01

    In quark nuclear physics (QNP), where hadrons and nuclei are described in terms of quarks and gluons, confinement and chiral symmetry breaking are the most fundamental phenomena. The dual Ginzburg-Landau (DGL) theory, which contains monopole fields as the most essential degrees of freedom and their condensation in the vacuum, is able to describe both phenomena. We discuss also the recovery of the chiral symmetry and the deconfinement phase transition at finite temperature in the DGL theory. As for the connection to QCD, we study the instanton configurations in the abelian gauge a la 't Hooft. We find a close connection between instantons and QCD monopoles. We demonstrate also the signature of confinement as the appearance of long monopole trajectories in the MA gauge for the case of dense instanton configurations. (orig.)

  4. Remarks on the Landau-Ginzburg potential and RG-flow for SU(2)-coset models

    International Nuclear Information System (INIS)

    Marzban, C.

    1989-09-01

    The existence of a Landau-Ginzburg (LG)-field for the SU(2)-coset models is motivated and conjectured. The general form of the LG potential for the A-series is found, and the RG-flow pattern suggested by this is shown to agree with that found by other authors, thereby further supporting the conjecture. (author). 17 refs

  5. Hc2 of anisotropy two-band superconductors by Ginzburg-Landau approach

    International Nuclear Information System (INIS)

    Udomsamuthirun, P.; Changjan, A.; Kumvongsa, C.; Yoksan, S.

    2006-01-01

    The purpose of this research is to study the upper critical field H c2 of two-band superconductors by two-band Ginzburg-Landau approach. The analytical formula of H c2 included anisotropy of order parameter and anisotropy of effective-mass are found. The parameters of the upper critical field in ab-plane (H c2 - bar ab ) and c-axis (H c2 - bar c ) can be found by fitting to the experimental data. Finally, we can find the ratio of upper critical field that temperature dependent in the range of experimental result

  6. The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation

    KAUST Repository

    Aguareles, M.

    2014-06-01

    In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.

  7. Dual Ginzburg-Landau theory and quark nuclear physics

    International Nuclear Information System (INIS)

    Toki, Hiroshi

    1999-01-01

    The elementary building blocks of matter are quarks. Hence, it is fundamental to describe hadrons and nuclei in terms of quarks and gluons, the subject of which is called Quark Nuclear Physics. The quark-dynamics is described by Quantum Chromodynamics (QCD). Our interest is the non-perturbative aspect of QCD as confinement, chiral symmetry breaking, hadronization etc. We introduce the dual Ginzburg-Landau theory (DGL), where the color monopole fields and their condensation is the QCD vacuum, play essential roles in describing these non-perturbative phenomena. We emphasize its connection to QCD through the use of the Abelian gauge. We apply the DGL theory to various observables. We discuss then the connection of the monopole fields with instantons, which are the classical solutions of the non-Abelian gauge theory and connect through the tunneling process QCD vacuum with different winding numbers. (author)

  8. Energie du type Ginzburg-Landau avec un terme de chevillage

    OpenAIRE

    AMARI, Nassima

    2010-01-01

    L’objectif de ce travail est l’étude d’un modèle bidimensionnel de Ginzburg-Landau avec un problème de l’ancrage (pinning) des vortex. La principale difficulté en réitérant l’approche faite par F. Béthuel, H. Brézis et F. Hélein, résulte du fait que la construction de mauvais disques ne soit pas évidente. Pour surmonter cette difficulté,on remplace le minimiseur u epsilon par v epsilon U epsilon. Cette substitution nous conduit à l'étude d'une énergie classique (qui correspond à p=1). ...

  9. Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems

    OpenAIRE

    Belmiloudi, Aziz

    2006-01-01

    We formulate and study robust control problems for a two-dimensional time-dependent Ginzburg-Landau model with Robin boundary conditions on phase-field parameter, which describes the phase transitions taking place in superconductor films with variable thickness. The objective of such study is to control the motion of vortices in the superconductor films by taking into account the influence of noises in data. Firstly, we introduce the perturbation problem of the nonlinear ...

  10. Parallel solution of the time-dependent Ginzburg-Landau equations and other experiences using BlockComm-Chameleon and PCN on the IBM SP, Intel iPSC/860, and clusters of workstations

    International Nuclear Information System (INIS)

    Coskun, E.

    1995-09-01

    Time-dependent Ginzburg-Landau (TDGL) equations are considered for modeling a thin-film finite size superconductor placed under magnetic field. The problem then leads to the use of so-called natural boundary conditions. Computational domain is partitioned into subdomains and bond variables are used in obtaining the corresponding discrete system of equations. An efficient time-differencing method based on the Forward Euler method is developed. Finally, a variable strength magnetic field resulting in a vortex motion in Type II High T c superconducting films is introduced. The authors tackled the problem using two different state-of-the-art parallel computing tools: BlockComm/Chameleon and PCN. They had access to two high-performance distributed memory supercomputers: the Intel iPSC/860 and IBM SP1. They also tested the codes using, as a parallel computing environment, a cluster of Sun Sparc workstations

  11. Ginzburg-Landau theory and the superconducting transition in thin, amorphous bismuth films

    International Nuclear Information System (INIS)

    Van Vechten, D.

    1979-01-01

    The Aslamasov-Larkin (AL) theory can be derived from a classical treatment of the conductivity due to short-lived statistical fluctuations into the superconducting state if one truncates the Ginzburg-Landau free energy density expression to read F[psi] = α 0 vertical barpsi vertical bar 2 + c 0 vertical bar del psi vertical bar 2 , where psi is the superconducting order parameter. The next largest term in the GL free energy is (b/2) (vertical bar psi vertical bar 2 ) 2 and is conventionally interpreted as representing the energy associated with interactions between the fluctuations. My dissertation consists of the calculation of the effect of this term on the fluctuation conductivity in three different approximations and the comparison of my predictions to the data of R.E. Glover III and M.K. Chien on thin amorphous bismuth films. The first approximation calculates the contribution to the fluctuations' self energy of the ''tadpole'' diagrams. This approximation yields a 4 parameter equation. Its fits were particularly outstanding for the films deposited on quartz or roughened glass substrates and only for two smooth glass substrates were there non-isolated data points that were not fit at the lowest temperatures measured. (The equation runs into trouble for these films at approximately R(T)/R/sub o/ =.08.) The values of the theoretical equation's fitting parameters were determined by a least squares method and turns out to depend on film thickness in the manner predicted by the theory. The next calculation improves the self energy approximation by including all the ''ring'' diagrams

  12. Rigorous study of the gap equation for an inhomogeneous superconducting state near T/sub c/

    International Nuclear Information System (INIS)

    Hu, C.R.

    1975-01-01

    An analytical study of the gap equation in the Bogoliubov formulation is presented. The normal-superconducting phase boundary is simulated by the expression Δ (R/sup =/) = Δ/sub infinity/ tanh / α Δ/sub infinity/z/v/sub f/) theta(z) where Δ/sub infinity/(t) is the equilibrium gap, theta (z) a unit step function and v/sub f/ the Fermi velocity. The Bogoliubov-de Gennes equations are solved in a nonperturbative WKBJ approximation. The gap equation is expanded near T/sub c/ in powers of Δ/sub infinity/ and the major term is of the same order as that given by the Ginzburg-Landau-Gor'kov approximation. Discrepancies in the two values are discussed in detail. It is concluded that the present technique reproduces the Ginzburg-Landau-Gor'kov results except within a BCS coherence length. 25 references

  13. Effect of colored noise on the critical dynamics of the Time-Dependent Landau-Ginzburg Model A

    International Nuclear Information System (INIS)

    Korutcheva, E.; Rubia, J. de la

    1999-08-01

    By using the dynamical renormalization-group method, we show that the introduction of an additive colored noise with weak long-range correlations in the Time-Dependent Landau-Ginzburg Model A, does not give perturbative corrections for the dynamical critical exponent at least up to order O(ε 2 ). This result differs for a system with random quenched impurities, where a similar type of impurity correlation leads to corrections even of order O(ε). (author)

  14. Multi-flux-tube system in the dual Ginzburg-Landau theory

    International Nuclear Information System (INIS)

    Ichie, H.; Suganuma, H.; Toki, H.

    1996-01-01

    We study the multi-flux-tube system in terms of the dual Ginzburg-Landau theory. We consider two periodic cases, where the directions of all the flux tubes are the same in one case and alternating in the other case for neighboring flux tubes. We formulate the multi-flux-tube system by regarding it as the system of two flux tubes penetrating through a two-dimensional spherical surface. We find the multi-flux-tube configuration becomes uniform above some critical flux-tube number density ρ c =1.3 endash 1.7 fm -2 . On the other hand, the inhomogeneity of the color electric distribution appears when the flux-tube density is smaller than ρ c . We study the inhomogeneity on the color electric distribution in relation with the flux-tube number density, and discuss the quark-gluon plasma formation process in ultrarelativistic heavy-ion collisions. copyright 1996 The American Physical Society

  15. Landau-Ginzburg orbifolds and symmetries of K3 CFTs

    Science.gov (United States)

    Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; Paquette, Natalie M.

    2017-01-01

    Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K3 string theory. To test and clarify these proposed K3-moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K3 sigma models. We compute K3ellipticgeneratwinedbydiscretesymmetriesthataremanifestintheUVdescription, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M 11 ⊂ 2 .M 12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Our results provide strong evidence for the relevance of umbral moonshine for K3 symmetries, as well as new hints for its eventual explanation.

  16. Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Dai, Jin; He, Jianfeng, E-mail: Antti.Niemi@physics.uu.se, E-mail: hjf@bit.edu.cn [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se, E-mail: hjf@bit.edu.cn [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108 Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200 Tours (France)

    2016-07-28

    The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Cα-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments.

  17. Conformational landscape of an amyloid intra-cellular domain and Landau-Ginzburg-Wilson paradigm in protein dynamics

    International Nuclear Information System (INIS)

    Dai, Jin; He, Jianfeng; Niemi, Antti J.

    2016-01-01

    The Landau-Ginzburg-Wilson paradigm is proposed as a framework, to investigate the conformational landscape of intrinsically unstructured proteins. A universal Cα-trace Landau free energy is deduced from general symmetry considerations, with the ensuing all-atom structure modeled using publicly available reconstruction programs Pulchra and Scwrl. As an example, the conformational stability of an amyloid precursor protein intra-cellular domain (AICD) is inspected; the reference conformation is the crystallographic structure with code 3DXC in Protein Data Bank (PDB) that describes a heterodimer of AICD and a nuclear multi-domain adaptor protein Fe65. Those conformations of AICD that correspond to local or near-local minima of the Landau free energy are identified. For this, the response of the original 3DXC conformation to variations in the ambient temperature is investigated, using the Glauber algorithm. The conclusion is that in isolation the AICD conformation in 3DXC must be unstable. A family of degenerate conformations that minimise the Landau free energy is identified, and it is proposed that the native state of an isolated AICD is a superposition of these conformations. The results are fully in line with the presumed intrinsically unstructured character of isolated AICD and should provide a basis for a systematic analysis of AICD structure in future NMR experiments.

  18. Landau-Ginzburg orbifolds and symmetries of K3 CFTs

    International Nuclear Information System (INIS)

    Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; Paquette, Natalie M.

    2017-01-01

    Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K 3 string theory. To test and clarify these proposed K 3 -moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K 3 sigma models. We compute K 3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M 11 c 2.M 12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Finally, our results provide strong evidence for the relevance of umbral moonshine for K 3 symmetries, as well as new hints for its eventual explanation.

  19. Localization and traces in open-closed topological Landau-Ginzburg models

    International Nuclear Information System (INIS)

    Herbst, Manfred; Lazaroiu, Calin-Iuliu

    2005-01-01

    We reconsider the issue of localization in open-closed B-twisted Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful analysis of zero-mode reduction, we show that the closed model allows for a one-parameter family of localization pictures, which generalize the standard residue representation. The parameter λ which indexes these pictures measures the area of worldsheets with S 2 topology, with the residue representation obtained in the limit of small area. In the boundary sector, we find a double family of such pictures, depending on parameters λ and μ which measure the area and boundary length of worldsheets with disk topology. We show that setting μ = 0 and varying λ interpolates between the localization picture of the B-model with a noncompact target space and a certain residue representation proposed recently. This gives a complete derivation of the boundary residue formula, starting from the explicit construction of the boundary coupling. We also show that the various localization pictures are related by a semigroup of homotopy equivalences

  20. Coarse graining from variationally enhanced sampling applied to the Ginzburg-Landau model

    Science.gov (United States)

    Invernizzi, Michele; Valsson, Omar; Parrinello, Michele

    2017-03-01

    A powerful way to deal with a complex system is to build a coarse-grained model capable of catching its main physical features, while being computationally affordable. Inevitably, such coarse-grained models introduce a set of phenomenological parameters, which are often not easily deducible from the underlying atomistic system. We present a unique approach to the calculation of these parameters, based on the recently introduced variationally enhanced sampling method. It allows us to obtain the parameters from atomistic simulations, providing thus a direct connection between the microscopic and the mesoscopic scale. The coarse-grained model we consider is that of Ginzburg-Landau, valid around a second-order critical point. In particular, we use it to describe a Lennard-Jones fluid in the region close to the liquid-vapor critical point. The procedure is general and can be adapted to other coarse-grained models.

  1. Critical initial-slip scaling for the noisy complex Ginzburg–Landau equation

    International Nuclear Information System (INIS)

    Liu, Weigang; Täuber, Uwe C

    2016-01-01

    We employ the perturbative fieldtheoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg–Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled nonlinear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose–Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross–Pitaevski or nonlinear Schrödinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau–Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent ‘initial-slip’ exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg–Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion. (paper)

  2. Analytic solutions to a family of boundary-value problems for Ginsburg-Landau type equations

    Science.gov (United States)

    Vassilev, V. M.; Dantchev, D. M.; Djondjorov, P. A.

    2017-10-01

    We consider a two-parameter family of nonlinear ordinary differential equations describing the behavior of a critical thermodynamic system, e.g., a binary liquid mixture, of film geometry within the framework of the Ginzburg-Landau theory by means of the order-parameter. We focus on the case in which the confining surfaces are strongly adsorbing but prefer different components of the mixture, i.e., the order-parameter tends to infinity at one of the boundaries and to minus infinity at the other one. We assume that the boundaries of the system are positioned at a finite distance from each other and give analytic solutions to the corresponding boundary-value problems in terms of Weierstrass and Jacobi elliptic functions.

  3. Spatiotemporal structure of pulsating solitons in the cubic-quintic Ginzburg-Landau equation: A novel variational formulation

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: smancas@mail.ucf.edu; Roy Choudhury, S. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: choudhur@longwood.cs.ucf.edu

    2009-04-15

    Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic-quintic Ginzburg-Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this paper, we address the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. First, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Next, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the starting formulation

  4. Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory

    International Nuclear Information System (INIS)

    Balatsky, A.

    1991-01-01

    In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-1/2 semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-1/2 semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to Su(2) κ=1 Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of ''spin rigidity'' of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacenmants. We argue that topological structure of Su(2) κ=1 Chern-Simons theory unambiguously dictates semion statistics of spinons. 19 refs

  5. The Landau theory of phase transitions

    Indian Academy of Sciences (India)

    2 Department of Computer Sci- ence, Indian ... in plasma physics, the Landau pole in quantum electro-. Keywords ... with Vitalyn Ginzburg, Landau made a milestone con- tribution to ..... This work was supported by the Physics Olympiad Pro-.

  6. Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals

    KAUST Repository

    Henao, Duvan; Majumdar, Apala

    2012-01-01

    We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892-905] and Millot and Pisante [J. Eur. Math. Soc. (JEMS), 12 (2010), pp. 1069- 1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg-Landau equations in superconductivity theory) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures. Copyright © by SIAM.

  7. Amplitude equations for a sub-diffusive reaction-diffusion system

    International Nuclear Information System (INIS)

    Nec, Y; Nepomnyashchy, A A

    2008-01-01

    A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points

  8. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

  9. Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser

    Energy Technology Data Exchange (ETDEWEB)

    Cunzheng, Ning; Haken, H [Inst. fuer Theoretische Physik und Synergetik, Univ. Stuttgart (Germany)

    1989-10-01

    A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super - form the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping. (orig.).

  10. Localization in nonuniform media: Exponential decay of the late-time Ginzburg-Landau impulse response

    International Nuclear Information System (INIS)

    Smith, E.

    1998-01-01

    Instanton methods have been used, in the context of a classical Ginzburg-Landau field theory, to compute the averaged density of states and probability Green close-quote s function for electrons scattered by statistically uniform site energy perturbations. At tree level, all states below some critical energy appear localized, and all states above extended. The same methods are applied here to macroscopically nonuniform systems, for which it is shown that localized and extended states can be coupled through a tunneling barrier created by the instanton background. Both electronic and acoustic systems are considered. An incoherent exponential decay is predicted for the late-time impulse response in both cases, valid for long-wavelength nonuniformity, and scaling relations are derived for the decay time constant as a function of energy or frequency and spatial dimension. The acoustic results are found to lie within a range of scaling relations obtained empirically from measurements of seismic coda, suggesting a connection between the universal properties of localization and the robustness of the observed scaling. The relation of instantons to the acoustic coherent-potential approximation is demonstrated in the recovery of the uniform limit. copyright 1998 The American Physical Society

  11. Exact solutions to the Mo-Papas and Landau-Lifshitz equations

    Science.gov (United States)

    Rivera, R.; Villarroel, D.

    2002-10-01

    Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

  12. Exact solutions to the Mo-Papas and Landau-Lifshitz equations

    International Nuclear Information System (INIS)

    Rivera, R.; Villarroel, D.

    2002-01-01

    Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics

  13. Vortex dynamics equation in type-II superconductors in a temperature gradient

    International Nuclear Information System (INIS)

    Vega Monroy, R.; Sarmiento Castillo, J.; Puerta Torres, D.

    2010-01-01

    In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

  14. Vortex dynamics equation in type-II superconductors in a temperature gradient

    Energy Technology Data Exchange (ETDEWEB)

    Vega Monroy, R.; Sarmiento Castillo, J. [Universidad del Atlantico, Barranquilla (Colombia). Facultad de Ciencias Basicas; Puerta Torres, D. [Universidad de Cartagena (Colombia). Facultad de Ciencias Exactas

    2010-12-15

    In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

  15. The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps

    International Nuclear Information System (INIS)

    Guo Boling; Hong Minchun.

    1992-05-01

    We prove a global existence of solutions for the Landau-Lifshitz equation of the ferromagnetic spin chain from an m-dimensional manifold M into the unit sphere S 2 of R 3 and establish some new links between harmonic maps and the solutions of the Landau-Lifshitz equation. (author). 25 refs

  16. Langevin equations with multiplicative noise: application to domain growth

    International Nuclear Information System (INIS)

    Sancho, J.M.; Hernandez-Machado, A.; Ramirez-Piscina, L.; Lacasta, A.M.

    1993-01-01

    Langevin equations of Ginzburg-Landau form with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hilliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical productions of the linear analysis. We also present simulation results for spinodal decomposition at large times. (author). 28 refs, 2 figs

  17. A New time Integration Scheme for Cahn-hilliard Equations

    KAUST Repository

    Schaefer, R.

    2015-06-01

    In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.

  18. A New time Integration Scheme for Cahn-hilliard Equations

    KAUST Repository

    Schaefer, R.; Smol-ka, M.; Dalcin, L; Paszyn'ski, M.

    2015-01-01

    In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.

  19. Transient analysis of scattering from ferromagnetic objects using Landau-Lifshitz-Gilbert and volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin

    2016-11-02

    An explicit marching on-in-time scheme for analyzing transient electromagnetic wave interactions on ferromagnetic scatterers is described. The proposed method solves a coupled system of time domain magnetic field volume integral and Landau-Lifshitz-Gilbert (LLG) equations. The unknown fluxes and fields are discretized using full and half Schaubert-Wilton-Glisson functions in space and bandlimited temporal interpolation functions in time. The coupled system is cast in the form of an ordinary differential equation and integrated in time using a PE(CE)m type linear multistep method to obtain the unknown expansion coefficients. Numerical results demonstrating the stability and accuracy of the proposed scheme are presented.

  20. Transient analysis of scattering from ferromagnetic objects using Landau-Lifshitz-Gilbert and volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan

    2016-01-01

    An explicit marching on-in-time scheme for analyzing transient electromagnetic wave interactions on ferromagnetic scatterers is described. The proposed method solves a coupled system of time domain magnetic field volume integral and Landau-Lifshitz-Gilbert (LLG) equations. The unknown fluxes and fields are discretized using full and half Schaubert-Wilton-Glisson functions in space and bandlimited temporal interpolation functions in time. The coupled system is cast in the form of an ordinary differential equation and integrated in time using a PE(CE)m type linear multistep method to obtain the unknown expansion coefficients. Numerical results demonstrating the stability and accuracy of the proposed scheme are presented.

  1. Comparison of numerical approaches to solve a Poincare-covariant Faddeev equation

    International Nuclear Information System (INIS)

    Alkofer, R.; Eichmann, G.; Krassnigg, A.; Schwinzerl, M.

    2006-01-01

    Full text: The quark core of Baryons can be described with the help of the numerical solution of the Poincare-Faddeev equation. Hereby the used elements, as e.g. the quark propagator are taken from non-perturbative studies of Landau gauge QCD. Different numerical approaches to solve in this way the relativistic three quark problem are compared and benchmarked results for the efficiency of different algorithms are presented. (author)

  2. Dyson-Schwinger equations and N = 4 SYM in Landau gauge

    Energy Technology Data Exchange (ETDEWEB)

    Maas, Axel; Zitz, Stefan [University of Graz, Institute of Physics, NAWI Graz, Graz (Austria)

    2016-03-15

    N = 4 Super Yang-Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang-Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory and the truncations of Dyson-Schwinger equations in ordinary Yang-Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang-Mills theories. We furthermore discuss which role the Gribov-Singer ambiguity in this context could play, should it exist in this theory. (orig.)

  3. On the proximity effect in a superconductive slab bordered by metal

    International Nuclear Information System (INIS)

    Liniger, W.

    1993-01-01

    The first Ginzburg-Landau equation for the order parameter ψ in the absence of magnetic fields is solved analytically for a superconducting slab of thickness 2d boardered by semi-infinite regions of normal metal at each face. The real-valued normalized wave function f=ψ/ψ ∞ depends only on the transversal spatial coordinate x, normalized with respect to the coherence length ξ of the superconductor, provided the de Gennes boundary condition df/dx=f/b is used. The closed-form solution expresses x as an elliptic integral of f, depending on the normalized parameters d and b. It is predicted theoretically that, for b c =arctan(1/b), the proximity effect is so strong that the superconductivity is completely suppressed. In fact, in this case, the first Ginzburg-Landau equation possesses only the trivial solution f≡0

  4. Dynamics of vortices in superconductors

    International Nuclear Information System (INIS)

    Weinan, E.

    1992-01-01

    We study the dynamics of vortices in type-II superconductors from the point of view of time-dependent Ginzburg-Landau equations. We outline a proof of existence, uniqueness and regularity of strong solutions for these equations. We then derive reduced systems of ODEs governing the motion of the vortices in the asymptotic limit of large Ginzburg-Landau parameter

  5. Bargmann representation for Landau levels in two dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Rohringer, Nina [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria); Burgdoerfer, Joachim [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria); Macris, Nicolas [Institut de Physique Theorique, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne (Switzerland)

    2003-04-11

    We present a formulation of the quantum mechanics of an electron gas confined to two dimensions in a strong magnetic field within the framework of the Hilbert space of analytic functions (Bargmann's space). Our approach extends the representation introduced by Girvin and Jach for the ground state to arbitrary Landau levels and to the regime of coupling between Landau levels. By projecting out the rapid cyclotron motion, the quantum mechanics of the slow guiding centre motion is converted into a system of coupled-channel equations describing the coupling between Landau levels due to the (disorder) potentials. In the limit of strong fields, the coupled-channel equations can be solved perturbatively. For the single-channel case we derive a WKB-like quantization condition for the one-dimensional motion along equipotential lines for arbitrary Landau levels. Two applications of this formalism are discussed: the weak-levitation problem in quantum Hall systems and a two-electron quantum dot in a strong magnetic field.

  6. Bargmann representation for Landau levels in two dimensions

    International Nuclear Information System (INIS)

    Rohringer, Nina; Burgdoerfer, Joachim; Macris, Nicolas

    2003-01-01

    We present a formulation of the quantum mechanics of an electron gas confined to two dimensions in a strong magnetic field within the framework of the Hilbert space of analytic functions (Bargmann's space). Our approach extends the representation introduced by Girvin and Jach for the ground state to arbitrary Landau levels and to the regime of coupling between Landau levels. By projecting out the rapid cyclotron motion, the quantum mechanics of the slow guiding centre motion is converted into a system of coupled-channel equations describing the coupling between Landau levels due to the (disorder) potentials. In the limit of strong fields, the coupled-channel equations can be solved perturbatively. For the single-channel case we derive a WKB-like quantization condition for the one-dimensional motion along equipotential lines for arbitrary Landau levels. Two applications of this formalism are discussed: the weak-levitation problem in quantum Hall systems and a two-electron quantum dot in a strong magnetic field

  7. Bargmann representation for Landau levels in two dimensions

    CERN Document Server

    Rohringer, N; Macris, N

    2003-01-01

    We present a formulation of the quantum mechanics of an electron gas confined to two dimensions in a strong magnetic field within the framework of the Hilbert space of analytic functions (Bargmann's space). Our approach extends the representation introduced by Girvin and Jach for the ground state to arbitrary Landau levels and to the regime of coupling between Landau levels. By projecting out the rapid cyclotron motion, the quantum mechanics of the slow guiding centre motion is converted into a system of coupled-channel equations describing the coupling between Landau levels due to the (disorder) potentials. In the limit of strong fields, the coupled-channel equations can be solved perturbatively. For the single-channel case we derive a WKB-like quantization condition for the one-dimensional motion along equipotential lines for arbitrary Landau levels. Two applications of this formalism are discussed: the weak-levitation problem in quantum Hall systems and a two-electron quantum dot in a strong magnetic field...

  8. Nonequilibrium theory of dirty, current-carrying superconductors: Phase-slip oscillators in narrow filaments near T/sub c/

    International Nuclear Information System (INIS)

    Watts-Tobin, R.J.; Kraehenbuehl, Y.; Kramer, L.

    1981-01-01

    General equations for the dynamic behavior of dirty superconductors in the Ginzburg--Landau regime Vertical BarT/sub c/-TVertical Bar<< T/sub c/ are derived from microscopic theory. In the immediate vicinity of T/sub c/ a local equilibrium approximation leads to a simple generalized time-dependent Ginzburg--Landau equation. The oscillatory phase-slip solutions presented previously are discussed in greater detail

  9. Thermodynamic properties of and Nuclei using modified Ginzburg-Landau theory

    Directory of Open Access Journals (Sweden)

    V Dehghani

    2016-09-01

    Full Text Available In this paper, formulation of Modified Ginsberg – Landau theory of second grade phase transitions has been expressed. Using this theory, termodynamic properties, such as heat capacity, energy, entropy and order parameters ofandnuclei has been investigated. In the heat capacity curve, calculated according to tempreture, a smooth peak is observed which is assumed to be a signature of transition from the paired phase to the normal phase of the nuclei. The same pattern is also observed in the experimental data of the heat capacity of the studied nuclei. Calculations of this model shows that, by increasing tempreture, expectation value of the order parameter tends to zero with smoother slip, comparing with Ginsberg – Landau theory. This indicates  that the pairing effect exists between nucleons even at high temperatures. The experimental data obtained confirms the results of the model qualitatively.

  10. Modeling of superconductors based on the timedependent Ginsburg-Landau equations

    Science.gov (United States)

    Grishakov, K. S.; Degtyarenko, P. N.; Degtyarenko, N. N.; Elesin, V. F.; Kruglov, V. S.

    2009-11-01

    Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors.

  11. Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

    Science.gov (United States)

    Yuzbashyan, Emil A.

    2018-05-01

    We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

  12. Analyses, algorithms, and computations for models of high-temperature superconductivity. Final technical report

    International Nuclear Information System (INIS)

    Gunzburger, M.D.; Peterson, J.S.

    1998-01-01

    Under the sponsorship of the Department of Energy, the authors have achieved significant progress in the modeling, analysis, and computation of superconducting phenomena. Their work has focused on mezoscale models as typified by the celebrated ginzburg-Landau equations; these models are intermediate between the microscopic models (that can be used to understand the basic structure of superconductors and of the atomic and sub-atomic behavior of these materials) and the macroscale, or homogenized, models (that can be of use for the design of devices). The models the authors have considered include a time dependent Ginzburg-Landau model, a variable thickness thin film model, models for high values of the Ginzburg-Landau parameter, models that account for normal inclusions and fluctuations and Josephson effects, and the anisotropic Ginzburg-Landau and Lawrence-Doniach models for layered superconductors, including those with high critical temperatures. In each case, they have developed or refined the models, derived rigorous mathematical results that enhance the state of understanding of the models and their solutions, and developed, analyzed, and implemented finite element algorithms for the approximate solution of the model equations

  13. Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

    Science.gov (United States)

    Simonucci, S.; Strinati, G. C.

    2014-02-01

    We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.

  14. Randomly forced CGL equation stationary measures and the inviscid limit

    CERN Document Server

    Kuksin, S

    2003-01-01

    We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable~$x$. Assuming that $\\dim x\\le4$, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schr\\"odinger equation.

  15. Solving Differential Equations in R: Package deSolve

    Science.gov (United States)

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

  16. Solving Differential Equations in R: Package deSolve

    NARCIS (Netherlands)

    Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.

    2010-01-01

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The

  17. Nucleation and dynamics of vortices in type-II superconductors

    International Nuclear Information System (INIS)

    Balley, R.E.

    1977-03-01

    The one- and two-dimensional Ginzburg-Landau equations are numerically integrated in a slab geometry, which is appropriate for comparison to experimental work done on films. When two-dimensional variations become energetically favorable, a vortex is found to nucleate and move to the center of the film with the Gibbs free energy decreasing during the process. An important process by which the energy is lowered during this nucleation procedure is found to be the savings in condensation energy arising from the shrinking size of the vortex core as it moves to the center of the film. The solutions of the Ginzburg-Landau equations are used to explain anomalies observed experimentally in the tunneling characteristics of thin films of PbIn. Excellent agreement between theory and experiment is found with the Ginzburg-Landau equations correctly predicting the field at which flux would first enter the films. We then use the Clem model of an isolated vortex to model vortex nucleation and dynamics under the influence of a transport current. The entry fields predicted by the model are found to be off by almost a factor of two but have the advantage of requiring simple computer programs for their solution, while the Ginzburg-Landau solutions require substantially more numerical work

  18. Ginsburg-Landau equation around the superconductor-insulator transition

    International Nuclear Information System (INIS)

    Ng, T.K.

    1991-01-01

    Based on the scaling theory of localization, we construct a Ginsburg-Landau (GL) equation for superconductors in an arbitrary strength of disordered potential. Using this GL equation, we reexamine the criteria for the superconductor-insulator transition and find that the transition to a localized superconductor can happen on both sides of the (normal) metal-insulator transition, in contrast to a previous prediction by Ma and Lee [Phys. Rev. B 32, 5658 (1985)] that the transition can only be on the insulator side. Furthermore, by comparing our theory with a recent scaling theory of dirty bosons by Fisher et al. [Phys. Rev. Lett. 64, 587 (1990)], we conclude that nontrivial crossover behavior in transport properties may occur in the vicinity of the superconductor-insulator transition

  19. Solutions without phase-slip for the Ginsburg-Landau equation

    International Nuclear Information System (INIS)

    Collet, P.; Eckmann, J.P.

    1992-01-01

    We consider the Ginsburg-Landau equation for a complex scalar field in one dimension and consider initial data which have two different stationary solutions as their limits in space as x→±∞. If these solutions are not very different, then we show that the initial data will evolve to a stationary solution by a 'phase melting' process which avoids 'phase slips,' i.e., which does not go through zero amplitude. (orig.)

  20. Analyses, algorithms, and computations for models of high-temperature superconductivity. Final report

    International Nuclear Information System (INIS)

    Du, Q.

    1997-01-01

    Under the sponsorship of the Department of Energy, the authors have achieved significant progress in the modeling, analysis, and computation of superconducting phenomena. The work so far has focused on mezoscale models as typified by the celebrated Ginzburg-Landau equations; these models are intermediate between the microscopic models (that can be used to understand the basic structure of superconductors and of the atomic and sub-atomic behavior of these materials) and the macroscale, or homogenized, models (that can be of use for the design of devices). The models they have considered include a time dependent Ginzburg-Landau model, a variable thickness thin film model, models for high values of the Ginzburg-landau parameter, models that account for normal inclusions and fluctuations and Josephson effects, and the anisotropic ginzburg-Landau and Lawrence-Doniach models for layered superconductors, including those with high critical temperatures. In each case, they have developed or refined the models, derived rigorous mathematical results that enhance the state of understanding of the models and their solutions, and developed, analyzed, and implemented finite element algorithms for the approximate solution of the model equations

  1. Relativistic Landau levels in the rotating cosmic string spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Cunha, M.S. [Universidade Estadual do Ceara, Grupo de Fisica Teorica (GFT), Fortaleza, CE (Brazil); Muniz, C.R. [Universidade Estadual do Ceara, Faculdade de Educacao, Ciencias e Letras de Iguatu, Iguatu, CE (Brazil); Christiansen, H.R. [Instituto Federal de Ciencia, Educacao e Tecnologia, IFCE Departamento de Fisica, Sobral (Brazil); Bezerra, V.B. [Universidade Federal da Paraiba-UFPB, Departamento de Fisica, Caixa Postal 5008, Joao Pessoa, PB (Brazil)

    2016-09-15

    In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin. (orig.)

  2. The dispersion-managed Ginzburg–Landau equation and its application to femtosecond lasers

    International Nuclear Information System (INIS)

    Biondini, Gino

    2008-01-01

    The complex Ginzburg–Landau equation has been used extensively to describe various nonequilibrium phenomena. In the context of lasers, it models the dynamics by averaging over the effects that take place inside the cavity. Pulses produced by Ti : sapphire femtosecond lasers, however, undergo significant changes in different parts of the cavity during each round-trip. The dynamics of such pulses is therefore not adequately described by an average model that does not take such changes into account. The purpose of this work is severalfold. We introduce the dispersion-managed Ginzburg–Landau equation (DMGLE) as an average model that describes the long-term dynamics of systems characterized by rapid variations of dispersion, nonlinearity and gain in a general setting, and we study the properties of the equation. We then explain how in particular the DMGLE arises for Ti : sapphire femtosecond lasers and we characterize its solutions. In particular, we show that, for moderate values of the gain/loss parameters, the solutions of the DMGLE are well approximated by those of the dispersion-managed nonlinear Schrödinger equation (DMNLSE), and the main effect of gain and loss dynamics is simply to select one among the one-parameter family of solutions of the DMNLSE

  3. Gamma-stability and vortex motion in type II superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Kurzke, Matthias; Spirn, Daniel

    2009-07-15

    We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative {gamma}-stability result relating the Ginzburg-Landau energy to the renormalized energy. (orig.)

  4. Gamma-stability and vortex motion in type II superconductors

    International Nuclear Information System (INIS)

    Kurzke, Matthias; Spirn, Daniel

    2009-01-01

    We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative Γ-stability result relating the Ginzburg-Landau energy to the renormalized energy. (orig.)

  5. The first critical field, Hc1perpendicularto, and the penetration depth in dirty superconducting S/N multilayers

    International Nuclear Information System (INIS)

    Golubov, A.A.; Krasnov, V.M.

    1992-01-01

    The proximity effect in dirty S/N multilayers is studied theoretically. The structure of the Abrikosov vortex and the first critical field, H c1 perpendicular to , in a perpendicular magnetic field is investigated. Our approach is based on solving Ginzburg-Landau and Usadel equations with boundary conditions applicable to real structures. It was shown that for highly conducting N-layers there exists a positive curvature on H c1 (T) dependences. (orig.)

  6. Criticality and novel quantum liquid phases in Ginzburg-Landau theories with compact and non-compact gauge fields

    Energy Technology Data Exchange (ETDEWEB)

    Smiseth, Jo

    2005-07-01

    The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)

  7. Landau fluid equations for electromagnetic and electrostatic fluctuations

    International Nuclear Information System (INIS)

    Hedrick, C.L.; Leboeuf, J.

    1992-01-01

    Closure relations are developed to allow approximate treatment of Landau damping and growth using fluid equations for both electrostatic and electromagnetic modes. The coefficients in these closure relations are related to approximations of the plasma dispersion function by ratios of polynomials. Thirteen different numerical sets of coefficients are given and explicitly related to previous fits to the plasma dispersion function. The application of the techniques presented in this paper is illustrated with the specific example of resistive g modes. Comparisons of full kinetic and approximate results are made for the solutions to the dispersion relation, radially resolved modes in sheared magnetic geometry, and the plasma dispersion function itself

  8. Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions

    DEFF Research Database (Denmark)

    Als-Nielsen, Jens Aage; Birgenau, R. J.

    1977-01-01

    By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...... in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated...

  9. Avoidance of a Landau pole by flat contributions in QED

    Energy Technology Data Exchange (ETDEWEB)

    Klaczynski, Lutz, E-mail: lutz.klaczynski@gmx.de [Department of Physics, Humboldt University Berlin, 12489 Berlin (Germany); Kreimer, Dirk, E-mail: kreimer@mathematik.hu-berlin.de [Alexander von Humboldt Chair in Mathematical Physics, Humboldt University, Berlin 12489 (Germany)

    2014-05-15

    We consider massless Quantum Electrodynamics in the momentum scheme and carry forward an approach based on Dyson–Schwinger equations to approximate both the β-function and the renormalized photon self-energy (Yeats, 2011). Starting from the Callan–Symanzik equation, we derive a renormalization group (RG) recursion identity which implies a non-linear ODE for the anomalous dimension and extract a sufficient but not necessary criterion for the existence of a Landau pole. This criterion implies a necessary condition for QED to have no such pole. Solving the differential equation exactly for a toy model case, we integrate the corresponding RG equation for the running coupling and find that even though the β-function entails a Landau pole it exhibits a flat contribution capable of decreasing its growth, in other cases possibly to the extent that such a pole is avoided altogether. Finally, by applying the recursion identity, we compute the photon propagator and investigate the effect of flat contributions on both spacelike and timelike photons. -- Highlights: •We present an approach to approximate both the β-function and the photon self-energy. •We find a sufficient criterion for the self-energy to entail the existence of a Landau pole. •We study non-perturbative ‘flat’ contributions that emerge within the context of our approach. •We discuss a toy model and how it is affected by flat contributions.

  10. Tunable Landau-Zener transitions using continuous- and chirped-pulse-laser couplings

    Science.gov (United States)

    Sarreshtedari, Farrokh; Hosseini, Mehdi

    2017-03-01

    The laser coupled Landau-Zener avoided crossing has been investigated with an aim towards obtaining the laser source parameters for precise controlling of the state dynamics in a two-level quantum system. The conventional Landau-Zener equation is modified for including the interaction of the system with a laser field during a bias energy sweep and the obtained Hamiltonian is numerically solved for the investigation of the two-state occupation probabilities. We have shown that in the Landau-Zener process, using an additional laser source with controlled amplitude, frequency, and phase, the system dynamics could be arbitrarily engineered. This is while, by synchronous frequency sweeping of a chirped-pulse laser, the system could be guided into a resonance condition, which again gives the remarkable possibility for precise tuning and controlling of the quantum system dynamics.

  11. Solving Differential Equations in R: Package deSolve

    Directory of Open Access Journals (Sweden)

    Karline Soetaert

    2010-02-01

    Full Text Available In this paper we present the R package deSolve to solve initial value problems (IVP written as ordinary differential equations (ODE, differential algebraic equations (DAE of index 0 or 1 and partial differential equations (PDE, the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR, DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1 to demonstrate the potential of using R for dynamic modeling, (2 to highlight typical uses of the different methods implemented and (3 to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to R’s high-level procedures. deSolve is the successor of package odesolve which will be deprecated in

  12. Dromion-like structures and stability analysis in the variable coefficients complex Ginzburg–Landau equation

    International Nuclear Information System (INIS)

    Wong, Pring; Pang, Li-Hui; Huang, Long-Gang; Li, Yan-Qing; Lei, Ming; Liu, Wen-Jun

    2015-01-01

    The study of the complex Ginzburg–Landau equation, which can describe the fiber laser system, is of significance for ultra-fast laser. In this paper, dromion-like structures for the complex Ginzburg–Landau equation are considered due to their abundant nonlinear dynamics. Via the modified Hirota method and simplified assumption, the analytic dromion-like solution is obtained. The partial asymmetry of structure is particularly discussed, which arises from asymmetry of nonlinear and dispersion terms. Furthermore, the stability of dromion-like structures is analyzed. Oscillation structure emerges to exhibit strong interference when the dispersion loss is perturbed. Through the appropriate modulation of modified exponent parameter, the oscillation structure is transformed into two dromion-like structures. It indicates that the dromion-like structure is unstable, and the coherence intensity is affected by the modified exponent parameter. Results in this paper may be useful in accounting for some nonlinear phenomena in fiber laser systems, and understanding the essential role of modified Hirota method

  13. Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

    International Nuclear Information System (INIS)

    Misguich, J.H.

    2004-04-01

    As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation

  14. Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

    Energy Technology Data Exchange (ETDEWEB)

    Misguich, J.H

    2004-04-01

    As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.

  15. Transport equation solving methods

    International Nuclear Information System (INIS)

    Granjean, P.M.

    1984-06-01

    This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

  16. Collisional width of giant resonances and interplay with Landau damping

    International Nuclear Information System (INIS)

    Bonasera, A.; Burgio, G.F.; Di Toro, M.; Wolter, H.H.

    1989-01-01

    We present a semiclassical method to calculate the widths of giant resonances. We solve a mean-field kinetic equation (Vlasov equation) with collision terms treated within the relaxation time approximation to construct a damped strength distribution for collective motions. The relaxation time is evaluated from the time evolution of distortions in the nucleon momentum distribution using a test-particle approach. The importance of an energy dependent nucleon-nucleon cross section is stressed. Results are shown for isoscalar giant quadrupole and octupole motions. A quite important interplay between self-consistent (Landau) and collisional damping is revealed

  17. Transversal expansion study in the Landau hydrodynamic

    International Nuclear Information System (INIS)

    Pottag, F.W.

    1984-01-01

    The system of equations in the frame of Landau's hydrodynamical model for multiparticle production at high energies is studied. Taking as a first approximation the one-dimensional exact due to Khalatnikov, and a special set of curvilinear coordinates, the radial part is separated from the longitudinal one in the equations of motion, and a system of partial differential equations (non-linear, hyperbolic) is obtained for the radial part. These equations are solved numerically by the method of caracteristics. The hydrodynamical variables are obtained over all the three-dimensional-flow region as well as its variation with the mass of the initially expanding system. Both, the transverse rapidity distribution of the fluid and the inclusive particle distribution at 90 0 in the center of mass system, are calculated. The last one is compared with recent experimental data. (author) [pt

  18. The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality

    KAUST Repository

    Majumdar, Apala

    2011-12-01

    We study small energy solutions within the Landau-de Gennes theory for nematic liquid crystals, subject to Dirichlet boundary conditions. We consider two-dimensional and three-dimensional domains separately. In the two-dimensional case, we establish the equivalence of the Landau-de Gennes and Ginzburg-Landau theory. In the three-dimensional case, we give a new definition of the defect set based on the normalized energy. In the threedimensional uniaxial case, we demonstrate the equivalence between the defect set and the isotropic set and prove the C 1,α-convergence of uniaxial small energy solutions to a limiting harmonic map, away from the defect set, for some 0 < a < 1, in the vanishing core limit. Generalizations for biaxial small energy solutions are also discussed, which include physically relevant estimates for the solution and its scalar order parameters. This work is motivated by the study of defects in liquid crystalline systems and their applications.

  19. A Fokker-Planck-Landau collision equation solver on two-dimensional velocity grid and its application to particle-in-cell simulation

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, E. S.; Chang, C. S., E-mail: cschang@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Korea Advanced Institute of Science and Technology, Yuseong-gu, DaeJeon 305-701 (Korea, Republic of)

    2014-03-15

    An approximate two-dimensional solver of the nonlinear Fokker-Planck-Landau collision operator has been developed using the assumption that the particle probability distribution function is independent of gyroangle in the limit of strong magnetic field. The isotropic one-dimensional scheme developed for nonlinear Fokker-Planck-Landau equation by Buet and Cordier [J. Comput. Phys. 179, 43 (2002)] and for linear Fokker-Planck-Landau equation by Chang and Cooper [J. Comput. Phys. 6, 1 (1970)] have been modified and extended to two-dimensional nonlinear equation. In addition, a method is suggested to apply the new velocity-grid based collision solver to Lagrangian particle-in-cell simulation by adjusting the weights of marker particles and is applied to a five dimensional particle-in-cell code to calculate the neoclassical ion thermal conductivity in a tokamak plasma. Error verifications show practical aspects of the present scheme for both grid-based and particle-based kinetic codes.

  20. Nonlinear stability of source defects in the complex Ginzburg–Landau equation

    International Nuclear Information System (INIS)

    Beck, Margaret; Nguyen, Toan T; Sandstede, Björn; Zumbrun, Kevin

    2014-01-01

    In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction–diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg–Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for Green's function, which allow one to close a nonlinear iteration scheme. (paper)

  1. Efficient positive, conservative, Maxwellian preserving and implicit difference schemes for the 1-D isotropic Fokker-Planck-Landau equation; Schemas positifs, implicites, conservant l'energie et les etats d'equilibre pour l'equation de Fokker-Planck-Landau isotrope

    Energy Technology Data Exchange (ETDEWEB)

    Buet, Ch. [CEA Bruyeres-le-Chatel, Dept. Sciences de la Simulation et de l' Information, Service Numerique Environnement et Constantes, 91 (France); Le Thanh, K.C. [CEA Bruyeres-le-Chatel, Service Physique des Plasmas et Electromagnetisme, 91 (France). Dept. de Physique Theorique et Appliquee

    2008-07-01

    The aim of this paper is to describe the discretization of the Fokker-Planck-Landau (FPL) collision term in the isotropic case, which models the self-collision for the electrons when they are totally isotropized by heavy particles background such as ions. The discussion focuses on schemes, which could preserve positivity, mass, energy and Maxwellian equilibrium. The Chang and Cooper method is widely used by plasma's physicists for the FPL equation (and for Fokker-Planck type equations). We present a new variant that is both positive and conservative contrary to the existing one's. We propose also a non Chang and Cooper 'type scheme on non-uniform grid, which is also both positive, conservative and equilibrium state preserving contrary to existing one's. The case of Coulombian potential is emphasized. We address also the problem of the time discretization. In particular we show how to recast some implicit methods to get band diagonal system and to solve it by direct method with a linear cost. (authors)

  2. Remarks on the three-level topological string theories

    International Nuclear Information System (INIS)

    Budzynski, R.J.

    1997-01-01

    A few observations concerning topological string theories at the string-tree level are presented: (1) The tree-level, large phase space solution of an arbitrary model is expressed in terms of a variational problem, with an ''action'' equal, at the solution, to the one-point function of the puncture operator, and found by solving equations of Gauss-Manin type; (2) For A k Landau-Ginzburg models, an extension to large phase space of the usual residue formula for three-point functions is given. (author)

  3. Construction of an exact solution of time-dependent Ginzburg ...

    Indian Academy of Sciences (India)

    time-dependent Ginzburg–Landau (TDGL) equations we have calculated the ... The prototype of such equations is the parabolic reaction diffusion equation [7,8] ..... It may be possible to compare the above results with suitable experiments, ...

  4. Fluctuations in the limit cycle state and the problem of phase chaos

    International Nuclear Information System (INIS)

    Szepfalusy, P.; Tel, T.

    1981-11-01

    Gaussian fluctuations and first order fluctuation corrections to the deterministic solution are investigated in the framework of the generalized Ginzburg-Landau type equation of motion exhibiting a hard mode transition leading a to homogeneous limit cycle state. It is shown that the stationary distribution of the fluctuations around the limit cycle is not of the form of a Ginzburg-Landau functional. The nature of the further instability in the post bifurcational region, resulting in the phase chaos in the deterministic problem, is found to be qualitatively changed by the presence of noise. (author)

  5. Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

    Science.gov (United States)

    Cameron, Stephen; Silvestre, Luis; Snelson, Stanley

    2018-05-01

    We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.

  6. Electron collisions in the trapped gyro-Landau fluid transport model

    International Nuclear Information System (INIS)

    Staebler, G. M.; Kinsey, J. E.

    2010-01-01

    Accurately modeling electron collisions in the trapped gyro-Landau fluid (TGLF) equations has been a major challenge. Insights gained from numerically solving the gyrokinetic equation have lead to a significant improvement of the low order TGLF model. The theoretical motivation and verification of this model with the velocity-space gyrokinetic code GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] will be presented. The improvement in the fidelity of TGLF to GYRO is shown to also lead to better prediction of experimental temperature profiles by TGLF for a dedicated collision frequency scan.

  7. The finite dimensional behaviour of the global attractors for the generalized Landau-Lifshitz equation on compact manifolds

    International Nuclear Information System (INIS)

    Guo Boling

    1994-01-01

    We prove the existence of the global attractors for the generalized Landau-Lifshitz equation on compact manifold M, and give the upper and lower estimates of their Hausdorff and fractal dimensions. (author). 18 refs

  8. Electric Conductivity of Hot and Dense Quark Matter in a Magnetic Field with Landau Level Resummation via Kinetic Equations

    Science.gov (United States)

    Fukushima, Kenji; Hidaka, Yoshimasa

    2018-04-01

    We compute the electric conductivity of quark matter at finite temperature T and a quark chemical potential μ under a magnetic field B beyond the lowest Landau level approximation. The electric conductivity transverse to B is dominated by the Hall conductivity σH. For the longitudinal conductivity σ∥, we need to solve kinetic equations. Then, we numerically find that σ∥ has only a mild dependence on μ and the quark mass mq. Moreover, σ∥ first decreases and then linearly increases as a function of B , leading to an intermediate B region that looks consistent with the experimental signature for the chiral magnetic effect. We also point out that σ∥ at a nonzero B remains within the range of the lattice-QCD estimate at B =0 .

  9. Landau damping in trapped Bose condensed gases

    Energy Technology Data Exchange (ETDEWEB)

    Jackson, B; Zaremba, E [Department of Physics, Queen' s University, Kingston, ON K7L 3N6 (Canada)

    2003-07-01

    We study Landau damping in dilute Bose-Einstein condensed gases in both spherical and prolate ellipsoidal harmonic traps. We solve the Bogoliubov equations for the mode spectrum in both of these cases, and calculate the damping by summing over transitions between excited quasiparticle states. The results for the spherical case are compared to those obtained in the Hartree-Fock (HF) approximation, where the excitations take on a single-particle character, and excellent agreement between the two approaches is found. We have also taken the semiclassical limit of the HF approximation and obtain a novel expression for the Landau damping rate involving the time-dependent self-diffusion function of the thermal cloud. As a final approach, we study the decay of a condensate mode by making use of dynamical simulations in which both the condensate and thermal cloud are evolved explicitly as a function of time. A detailed comparison of all these methods over a wide range of sample sizes and trap geometries is presented.

  10. Enhancement of the Accelerating Gradient in Superconducting Microwave Resonators

    Energy Technology Data Exchange (ETDEWEB)

    Checchin, Mattia [Fermilab; Grassellino, Anna [Fermilab; Martinello, Martina [IIT, Chicago; Posen, Sam [Fermilab; Romanenko, Alexander [Fermilab; Zasadzinski, John [IIT, Chicago (main)

    2017-05-01

    The accelerating gradient of superconducting resonators can be enhanced by engineering the thickness of a dirty layer grown at the cavity's rf surface. In this paper the description of the physics behind the accelerating gradient enhancement by meaning of the dirty layer is carried out by solving numerically the the Ginzburg-Landau (GL) equations for the layered system. The calculation shows that the presence of the dirty layer stabilizes the Meissner state up to the lower critical field of the bulk, increasing the maximum accelerating gradient.

  11. Nucleación de vórtices y antivórtices en películas superconductoras con nanoestructuras magnéticas

    Directory of Open Access Journals (Sweden)

    J. Barba-Ortega

    2011-01-01

    Full Text Available In this work, we investigated theoretically the configuration of vortex and antivortex configuration in a magnetically nanostructured superconducting film by solving numerically the system of nonlinear time dependent Ginzburg-Landau differential equations. Interesting vortex and anti-vortex structures are found when a thin superconducting film is covered by an array of magnetic dipoles. We show that due to the (anti vortices and the supercurrents induced by the magnetic dipoles, the critical current increases if the sample is exposed to an external magnetic field, if not to what happens in conventional superconductors.

  12. Non-radially symmetric solutions to the Ginzburg-Landau equation

    CERN Document Server

    Ovchinnikov, Yu N

    2000-01-01

    We study an atom with finitely many energy levels in contact with a heat bath consisting of photons (black body radiation) at a temperature $T >0$. The dynamics of this system is described by a Liouville operator, or thermal Hamiltonian, which is the sum of an atomic Liouville operator, of a Liouville operator describing the dynamics of a free, massless Bose field, and a local operator describing the interactions between the atom and the heat bath. We show that an arbitrary initial state which is normal with respect to the equilibrium state of the uncoupled system at temperature $T$ converges to an equilibrium state of the coupled system at the same temperature, as time tends to $+ \\infty$

  13. Numerical solutions of the Vlasov equation

    International Nuclear Information System (INIS)

    Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

    1985-01-01

    A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)

  14. The Landau-Lifshitz equation describes the Ising spin correlation function in the free-fermion model

    CERN Document Server

    Rutkevich, S B

    1998-01-01

    We consider time and space dependence of the Ising spin correlation function in a continuous one-dimensional free-fermion model. By the Ising spin we imply the 'sign' variable, which takes alternating +-1 values in adjacent domains bounded by domain walls (fermionic world paths). The two-point correlation function is expressed in terms of the solution of the Cauchy problem for a nonlinear partial differential equation, which is proved to be equivalent to the exactly solvable Landau-Lifshitz equation. A new zero-curvature representation for this equation is presented. In turn, the initial condition for the Cauchy problem is given by the solution of a nonlinear ordinary differential equation, which has also been derived. In the Ising limit the above-mentioned partial and ordinary differential equations reduce to the sine-Gordon and Painleve III equations, respectively. (author)

  15. A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates

    KAUST Repository

    Sierra Nunez, Jesus Alfredo

    2018-05-16

    The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the

  16. Vortex properties of mesoscopic superconducting samples

    Energy Technology Data Exchange (ETDEWEB)

    Cabral, Leonardo R.E. [Laboratorio de Supercondutividade e Materiais Avancados, Departamento de Fisica, Universidade Federal de Pernambuco, Recife 50670-901 (Brazil); Barba-Ortega, J. [Grupo de Fi' sica de Nuevos Materiales, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia); Souza Silva, C.C. de [Laboratorio de Supercondutividade e Materiais Avancados, Departamento de Fisica, Universidade Federal de Pernambuco, Recife 50670-901 (Brazil); Albino Aguiar, J., E-mail: albino@df.ufpe.b [Laboratorio de Supercondutividade e Materiais Avancados, Departamento de Fisica, Universidade Federal de Pernambuco, Recife 50670-901 (Brazil)

    2010-10-01

    In this work we investigated theoretically the vortex properties of mesoscopic samples of different geometries, submitted to an external magnetic field. We use both London and Ginzburg-Landau theories and also solve the non-linear Time Dependent Ginzburg-Landau equations to obtain vortex configurations, equilibrium states and the spatial distribution of the superconducting electron density in a mesoscopic superconducting triangle and long prisms with square cross-section. For a mesoscopic triangle with the magnetic field applied perpendicularly to sample plane the vortex configurations were obtained by using Langevin dynamics simulations. In most of the configurations the vortices sit close to the corners, presenting twofold or three-fold symmetry. A study of different meta-stable configurations with same number of vortices is also presented. Next, by taking into account de Gennes boundary conditions via the extrapolation length, b, we study the properties of a mesoscopic superconducting square surrounded by different metallic materials and in the presence of an external magnetic field applied perpendicularly to the square surface. It is determined the b-limit for the occurrence of a single vortex in a mesoscopic square of area d{sup 2}, for 4{xi}(0){<=}d{<=}10{xi}(0).

  17. The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

    Science.gov (United States)

    Clark, S. E.; Oishi, Jeffrey S.

    2017-05-01

    The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

  18. The interaction between d-dot's

    International Nuclear Information System (INIS)

    Hirayama, Masaki; Machida, Masahiko; Koyama, Tomio; Ishida, Takekazu; Kato, Masaru

    2005-01-01

    We investigated the interaction between two square d-dot's. The d-dot is the nano-scaled superconducting composite structure that is made of a d-wave superconducting dot embedded in the s-wave superconducting matrix. In the numerical calculation, using the finite element method, we solved the two-components Ginzburg-Landau equation self-consistently. We obtained two kinds of solutions, which can be considered as ferromagnetic and antiferromagnetic configurations, when two d-dot's are separated parallel and diagonally. Also we discuss the applicability of d-dot's as an artificial spin system where the interactions can be controlled by the fabrication

  19. The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals

    KAUST Repository

    MAJUMDAR, APALA

    2011-09-06

    We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau-de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg-Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg-Landau limit for the Landau-de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau-de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities. © Copyright Cambridge University Press 2011.

  20. The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals

    KAUST Repository

    MAJUMDAR, APALA

    2011-01-01

    We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau-de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg-Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg-Landau limit for the Landau-de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau-de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities. © Copyright Cambridge University Press 2011.

  1. Quantum corrections to nonlinear ion acoustic wave with Landau damping

    Energy Technology Data Exchange (ETDEWEB)

    Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)

    2014-07-15

    Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.

  2. Connectivity and superconductivity

    CERN Document Server

    Rubinstein, Jacob

    2000-01-01

    The motto of connectivity and superconductivity is that the solutions of the Ginzburg--Landau equations are qualitatively influenced by the topology of the boundaries, as in multiply-connected samples. Special attention is paid to the "zero set", the set of the positions (also known as "quantum vortices") where the order parameter vanishes. The effects considered here usually become important in the regime where the coherence length is of the order of the dimensions of the sample. It takes the intuition of physicists and the awareness of mathematicians to find these new effects. In connectivity and superconductivity, theoretical and experimental physicists are brought together with pure and applied mathematicians to review these surprising results. This volume is intended to serve as a reference book for graduate students and researchers in physics or mathematics interested in superconductivity, or in the Schrödinger equation as a limiting case of the Ginzburg--Landau equations.

  3. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  4. Electron Landau damping of ion Bernstein waves in tokamak plasmas

    International Nuclear Information System (INIS)

    Brambilla, M.

    1998-01-01

    Absorption of ion Bernstein (IB) waves by electrons is investigated. These waves are excited by linear mode conversion in tokamak plasmas during fast wave (FW) heating and current drive experiments in the ion cyclotron range of frequencies. Near mode conversion, electromagnetic corrections to the local dispersion relation largely suppress electron Landau damping of these waves, which becomes important again, however, when their wavelength is comparable to the ion Larmor radius or shorter. The small Larmor radius wave equations solved by most numerical codes do not correctly describe the onset of electron Landau damping at very short wavelengths, and these codes, therefore, predict very little damping of IB waves, in contrast to what one would expect from the local dispersion relation. We present a heuristic, but quantitatively accurate, model which allows account to be taken of electron Landau damping of IB waves in such codes, without affecting the damping of the compressional wave or the efficiency of mode conversion. The possibilities and limitations of this approach are discussed on the basis of a few examples, obtained by implementing this model in the toroidal axisymmetric full wave code TORIC. (author)

  5. Stochastic Landau equation with time-dependent drift

    International Nuclear Information System (INIS)

    Swift, J.B.; Hohenberg, P.C.; Ahlers, G.

    1991-01-01

    The stochastic differential equation τ 0 ∂ tA =ε(t)A-g 3 A 3 +bar f(t), where bar f(t) is Gaussian white noise, is studied for arbitrary time dependence of ε(t). In particular, cases are considered where ε(t) goes through the bifurcation of the deterministic system, which occurs at ε=0. In the limit of weak noise an approximate analytic expression generalizing earlier work of Suzuki [Phys. Lett. A 67, 339 (1978); Prog. Theor. Phys. (Kyoto) Suppl. 64, 402 (1978)] is obtained for the time-dependent distribution function P(A,t). The results compare favorably with a numerical simulation of the stochastic equation for the case of a linear ramp (both increasing and decreasing) and for a periodic time dependence of ε(t). The procedure can be generalized to an arbitrary deterministic part ∂ tA =D(A,t)+bar f(t), but the deterministic equation may then have to be solved numerically

  6. Students’ difficulties in solving linear equation problems

    Science.gov (United States)

    Wati, S.; Fitriana, L.; Mardiyana

    2018-03-01

    A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

  7. Interaction of langmuir and ion acoustic waves

    International Nuclear Information System (INIS)

    Lee, Hee Jae

    1991-01-01

    Interaction of Langmuir and ion acoustic waves in a plasma is described by Landau-Ginzburg type of equation when the group velocity of the Langmuir wave is equal to the wave velocity of ion acoustic wave. (Author)

  8. On Landau damping

    KAUST Repository

    Mouhot, Clément

    2011-09-01

    Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of non-linear echoes; sharp "deflection" estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the non-linear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications. Finally, we extend these results to some Gevrey (non-analytic) distribution functions. © 2011 Institut Mittag-Leffler.

  9. Real-time relaxation and kinetics in hot scalar QED: Landau damping

    International Nuclear Information System (INIS)

    Boyanovsky, D.; Vega, H.J. de; Holman, R.; Kumar, S.P.; Pisarski, R.D.

    1998-01-01

    The real time evolution of non-equilibrium expectation values with soft length scales ∼k -1 >(eT) -1 is solved in hot scalar electrodynamics, with a view towards understanding relaxational phenomena in the QGP and the electroweak plasma. We find that the gauge invariant non-equilibrium expectation values relax via power laws to asymptotic amplitudes that are determined by the quasiparticle poles. The long time relaxational dynamics and relevant time scales are determined by the behavior of the retarded self-energy not at the small frequencies, but at the Landau damping thresholds. This explains the presence of power laws and not of exponential decay. In the process we rederive the HTL effective action using non-equilibrium field theory. Furthermore we obtain the influence functional, the Langevin equation and the fluctuation-dissipation theorem for the soft modes, identifying the correlators that emerge in the classical limit. We show that a Markovian approximation fails to describe the dynamics both at short and long times. We find that the distribution function for soft quasiparticles relaxes with a power law through Landau damping. We also introduce a novel kinetic approach that goes beyond the standard Boltzmann equation by incorporating off-shell processes and find that the distribution function for soft quasiparticles relaxes with a power law through Landau damping. We find an unusual dressing dynamics of bare particles and anomalous (logarithmic) relaxation of hard quasiparticles. copyright 1998 The American Physical Society

  10. Cognitive Load in Algebra: Element Interactivity in Solving Equations

    Science.gov (United States)

    Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

    2015-01-01

    Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

  11. Applying homotopy analysis method for solving differential-difference equation

    International Nuclear Information System (INIS)

    Wang Zhen; Zou Li; Zhang Hongqing

    2007-01-01

    In this Letter, we apply the homotopy analysis method to solving the differential-difference equations. A simple but typical example is applied to illustrate the validity and the great potential of the generalized homotopy analysis method in solving differential-difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the differential-difference equations

  12. [The physics of cellular automata and coherence and chaos in classical many-body systems

    International Nuclear Information System (INIS)

    1992-01-01

    This report contains short discussions on the following topics: non-variational effects in a Ginzburg-Landau equation; algebraic correlations in conserved chaotic systems; chaotic interface models of turbulence; algebraic correlations in coupled order parameter systems; and dynamics of Josephson Junction arrays

  13. Finite-temperature effects in helical quantum turbulence

    Science.gov (United States)

    Clark Di Leoni, Patricio; Mininni, Pablo D.; Brachet, Marc E.

    2018-04-01

    We perform a study of the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the stochastic Ginzburg-Landau equations, using up to 40963 grid points with a pseudospectral method. We show that for temperatures close to the critical one, the fluid described by these equations can act as a classical viscous flow, with the decay of the incompressible kinetic energy and the helicity becoming exponential. The transition from this behavior to the one observed at zero temperature is smooth as a function of temperature. Moreover, the presence of strong thermal effects can inhibit the development of a proper turbulent cascade. We provide Ansätze for the effective viscosity and friction as a function of the temperature.

  14. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    Science.gov (United States)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  15. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  16. New method for solving three-dimensional Schroedinger equation

    International Nuclear Information System (INIS)

    Melezhik, V.S.

    1992-01-01

    A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables, Ω, from X={R,Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigenvalue) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and 'dipole' scatterer, a hydrogen atom in a homogenous magnetic field) and for a three-dimensional problem of the helium-atom bound states. (author)

  17. Parallel Algorithm Solves Coupled Differential Equations

    Science.gov (United States)

    Hayashi, A.

    1987-01-01

    Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

  18. Vortex-antivortex patterns in mesoscopic superconductors

    International Nuclear Information System (INIS)

    Teniers, Gerd; Moshchalkov, V.V.; Chibotaru, L.F.; Ceulemans, Arnout

    2003-01-01

    We have studied the nucleation of superconductivity in mesoscopic structures of different shape (triangle, square and rectangle). This was made possible by using an analytical gauge transformation for the vector potential A which gives A n =0 for the normal component along the boundary line of the rectangle. As a consequence the superconductor-vacuum boundary condition reduces to the Neumann boundary condition. By solving the linearized Ginzburg-Landau equation with this boundary condition we have determined the field-temperature superconducting phase boundary and the corresponding vortex patterns. The comparison of these patterns for different structures demonstrates that the critical parameters of a superconductor can be manipulated and fine-tuned through nanostructuring

  19. Theory of phase-slip processes in thin and dirty current-carrying superconducting wires: Deviations from local equilibrium

    International Nuclear Information System (INIS)

    Kraehenbuehl, Y.

    1983-01-01

    Oscillatory phase-slip solution of a set of integrodifferential equations describing time-dependent processes in dirty superconductors in the Ginzburg-Landau regime are found numerically very near Tsub(c). Deviations from local equilibrium improve the agreement with observed V-I curves. (orig.)

  20. A Photon Free Method to Solve Radiation Transport Equations

    International Nuclear Information System (INIS)

    Chang, B

    2006-01-01

    The multi-group discrete-ordinate equations of radiation transfer is solved for the first time by Newton's method. It is a photon free method because the photon variables are eliminated from the radiation equations to yield a N group XN direction smaller but equivalent system of equations. The smaller set of equations can be solved more efficiently than the original set of equations. Newton's method is more stable than the Semi-implicit Linear method currently used by conventional radiation codes

  1. Nonlinear dynamics near the stability margin in rotating pipe flow

    Science.gov (United States)

    Yang, Z.; Leibovich, S.

    1991-01-01

    The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

  2. Solving Absolute Value Equations Algebraically and Geometrically

    Science.gov (United States)

    Shiyuan, Wei

    2005-01-01

    The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

  3. Landau damping of dust acoustic solitary waves in nonthermal plasmas

    Science.gov (United States)

    Ghai, Yashika; Saini, N. S.; Eliasson, B.

    2018-01-01

    Dust acoustic (DA) solitary and shock structures have been investigated under the influence of Landau damping in a dusty plasma containing two temperature nonthermal ions. Motivated by the observations of Geotail spacecraft that reported two-temperature ion population in the Earth's magnetosphere, we have investigated the effect of resonant wave-particle interactions on DA nonlinear structures. The Korteweg-de Vries (KdV) equation with an additional Landau damping term is derived and its analytical solution is presented. The solution has the form of a soliton whose amplitude decreases with time. Further, we have illustrated the influence of Landau damping and nonthermality of the ions on DA shock structures by a numerical solution of the Landau damping modified KdV equation. The study of the time evolution of shock waves suggests that an initial shock-like pulse forms an oscillatory shock at later times due to the balance of nonlinearity, dispersion, and dissipation due to Landau damping. The findings of the present investigation may be useful in understanding the properties of nonlinear structures in the presence of Landau damping in dusty plasmas containing two temperature ions obeying nonthermal distribution such as in the Earth's magnetotail.

  4. Split of the superconducting transition and magnetism in UPt3

    International Nuclear Information System (INIS)

    Marikhin, V.G.

    1992-01-01

    A possible reason for splitting the superconducting phase transition in UPt 3 is discussed. The strong coupling of conduction electrons with uranium atom magnetic moments may be such a cause. The given assertion is based on the simple model described by the two-component order parameter φ Ginzburg -Landau functional. The Ginzburg - Landau functional without coupling has the whole symmetry D 6h of hexagonal crystal. Due to the presence of uranium atom magnetic moments M the symmetry is broken locally with the coupling term γ|Mφ| 2 in the Ginzburg - Landau functional. Averaging over the vector M configurations with the involment of the finite correlation radius a is performed. The inequality a 6h . This means that in a real crystal the hexagonal symmetry is not broken at the scales larger ξ. In the framework of the given theory the expressions for the specific heat jumps and equation combining the upper critical field H c2 and the phase transition split ΔT c with the pressure variation are obtained. The difficulties connencted with the small experimental magnitude of uranium atom magnetic moments are discussed

  5. Simplified Model of Nonlinear Landau Damping

    International Nuclear Information System (INIS)

    Yampolsky, N.A.; Fisch, N.J.

    2009-01-01

    The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.

  6. Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations

    International Nuclear Information System (INIS)

    Stefanski, B. Jr.; Tseytlin, A.A.

    2004-01-01

    We consider AdS 5 x S 5 string states with several large angular momenta along AdS 5 and S 5 directions which are dual to single-trace Super-Yang-Mills (SYM) operators built out of chiral combinations of scalars and covariant derivatives. In particular, we focus on the SU(3) sector (with three spins in S 5 ) and the SL(2) sector (with one spin in AdS 5 and one in S 5 ), generalizing recent work hep-th/0311203 and hep-th/0403120 on the SU(2) sector with two spins in S 5 . We show that, in the large spin limit and at the leading order in the effective coupling expansion, the string sigma model equations of motion reduce to matrix Landau-Lifshitz equations. We then demonstrate that the coherent-state expectation value of the one-loop SYM dilatation operator restricted to the corresponding sector of single trace operators is also effectively described by the same equations. This implies a universal leading order equivalence between string energies and SYM anomalous dimensions, as well as a matching of integrable structures. We also discuss the more general 5-spin sector and comment on SO(6) states dual to non-chiral scalar operators. (author)

  7. Effective Ginzburg–Landau free energy functional for multi-band isotropic superconductors

    International Nuclear Information System (INIS)

    Grigorishin, Konstantin V.

    2016-01-01

    Highlights: • The intergradient coupling of order parameters in a two-band superconductor plays important role and cannot be neglected. • A two-band superconductor must be characterized with a single coherence length and a single Ginzburg–Landau parameter. • Type-1.5 superconductors are impossible. • The free energy functional for a multi-band superconductor can be reduced to the effective single-band Ginzburg–Landau functional. - Abstract: It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role – such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg–Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate method for solving of set of GL equations for a multi-band superconductor has been developed: using the result about the drag effect it has been shown that the free-energy functional for a multi-band superconductor can be reduced to the GL functional for an effective single-band superconductor.

  8. Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

    Science.gov (United States)

    Tóth, Gyula I.

    2016-09-01

    In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

  9. Variational iteration method for solving coupled-KdV equations

    International Nuclear Information System (INIS)

    Assas, Laila M.B.

    2008-01-01

    In this paper, the He's variational iteration method is applied to solve the non-linear coupled-KdV equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converge to the exact solution of the coupled-KdV equations. This procedure is a powerful tool for solving coupled-KdV equations

  10. Modulated Langmuir waves and nonlinear Landau damping

    International Nuclear Information System (INIS)

    Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.

    1975-01-01

    The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)

  11. Ten themes of viscous liquid dynamics

    DEFF Research Database (Denmark)

    Dyre, J. C.

    2007-01-01

    Ten ‘themes' of viscous liquid physics are discussed with a focus on how they point to a general description of equilibrium viscous liquid dynamics (i.e., fluctuations) at a given temperature. This description is based on standard time-dependent Ginzburg-Landau equations for the density fields...

  12. Exp-function method for solving Fisher's equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, X-W [Department of Mathematics, Kunming Teacher' s College, Kunming, Yunnan 650031 (China)], E-mail: km_xwzhou@163.com

    2008-02-15

    There are many methods to solve Fisher's equation, but each method can only lead to a special solution. In this paper, a new method, namely the exp-function method, is employed to solve the Fisher's equation. The obtained result includes all solutions in open literature as special cases, and the generalized solution with some free parameters might imply some fascinating meanings hidden in the Fisher's equation.

  13. Some applications of nonlinear diffusion to processing of dynamic evolution images

    International Nuclear Information System (INIS)

    Goltsov, Alexey N.; Nikishov, Sergey A.

    1997-01-01

    Model nonlinear diffusion equation with the most simple Landau-Ginzburg free energy functional was applied to locate boundaries between meaningful regions of low-level images. The method is oriented to processing images of objects that are a result of dynamic evolution: images of different organs and tissues obtained by radiography and NMR methods, electron microscope images of morphogenesis fields, etc. In the methods developed by us, parameters of the nonlinear diffusion model are chosen on the basis of the preliminary treatment of the images. The parameters of the Landau-Ginzburg free energy functional are extracted from the structure factor of the images. Owing to such a choice of the model parameters, the image to be processed is located in the vicinity of the steady-state of the diffusion equation. The suggested method allows one to separate distinct structures having specific space characteristics from the whole image. The method was applied to processing X-ray images of the lung

  14. Generalized Landau-Lifshitz models on the interval

    International Nuclear Information System (INIS)

    Doikou, Anastasia; Karaiskos, Nikos

    2011-01-01

    We study the classical generalized gl n Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl 2 L-L model. Novel expressions of the modified Lax pairs associated to the integrals of motion are also extracted. The relevant equations of motion with the corresponding boundary conditions are determined. Dynamical integrable boundary conditions are also examined within this spirit. Then the generalized isotropic and anisotropic gl n Landau-Lifshitz models are considered, and novel expressions of the boundary Hamiltonians and the relevant equations of motion and boundary conditions are derived.

  15. Birth–death process of local structures in defect turbulence described by the one-dimensional complex Ginzburg–Landau equation

    Energy Technology Data Exchange (ETDEWEB)

    Uchiyama, Yusuke, E-mail: r1230160@risk.tsukuba.ac.jp; Konno, Hidetoshi

    2014-04-01

    Defect turbulence described by the one-dimensional complex Ginzburg–Landau equation is investigated and analyzed via a birth–death process of the local structures composed of defects, holes, and modulated amplitude waves (MAWs). All the number statistics of each local structure, in its stationary state, are subjected to Poisson statistics. In addition, the probability density functions of interarrival times of defects, lifetimes of holes, and MAWs show the existence of long-memory and some characteristic time scales caused by zigzag motions of oscillating traveling holes. The corresponding stochastic process for these observations is fully described by a non-Markovian master equation.

  16. Are the dressed gluon and ghost propagators in the Landau gauge presently determined in the confinement regime of QCD?

    International Nuclear Information System (INIS)

    Pennington, M. R.; Wilson, D. J.

    2011-01-01

    The gluon and ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find that a nontrivial full ghost-gluon vertex is required in the vanishing gluon momentum limit. The self-consistent solutions we obtain correspond to having a masslike term in the gluon propagator dressing, in agreement with similar studies supporting the long-held proposal of Cornwall.

  17. Solving Variable Coefficient Fourth-Order Parabolic Equation by ...

    African Journals Online (AJOL)

    Solving Variable Coefficient Fourth-Order Parabolic Equation by Modified initial guess Variational ... variable coefficient fourth order parabolic partial differential equations. The new method shows rapid convergence to the exact solution.

  18. A fast non-Fourier method for Landau-fluid operators

    Energy Technology Data Exchange (ETDEWEB)

    Dimits, A. M., E-mail: dimits1@llnl.gov; Joseph, I.; Umansky, M. V. [Lawrence Livermore National Laboratory, L-637, P.O. Box 808, Livermore, California 94511-0808 (United States)

    2014-05-15

    An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of “delocalization kernels” [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost and memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUT++ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUT++ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUT++ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.

  19. Stability and dynamics of spatio-temporal structures. Progress report, September 15, 1993--September 14, 1994

    Energy Technology Data Exchange (ETDEWEB)

    Riecke, H.

    1994-05-01

    Goal is to contribute to understanding of localized spatial and spatio-temporal structures far from thermodynamic equilibrium. Here we report on our progress in the study of three classes of systems. (1) We have studied cellular flame structures arising in a circular burner. Using numerical computations we have found a number of traveling-wave structures in which different cells undergo different motion. Most strikingly, we have found a localized wave traveling through the array of steady cells. Results are interpreted using various asymptotic approaches. They are in qualitative agreement with recent experiments. (2) We have continued our investigation of localized waves in binary-mixture convection. Starting from the extended Ginzburg-Landau equations introduced earlier, we have derived equations of motion for interacting fronts connecting the conductive and the convective state. These equations reveal a repulsive interaction between the fronts which implies a new localization mechanism for waves. It is solely due to the long-wavelength mode specific to the extended Ginzburg-Landau equations. The stability properties of the resulting localized waves are in qualitative agreement with very recent experiments. (3) We have extended our investigation of domain structures to include their temporal evolution.

  20. Sinc-collocation method for solving the Blasius equation

    International Nuclear Information System (INIS)

    Parand, K.; Dehghan, Mehdi; Pirkhedri, A.

    2009-01-01

    Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.

  1. Local control of globally competing patterns in coupled Swift-Hohenberg equations

    Science.gov (United States)

    Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, Markus

    2018-04-01

    We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

  2. Scalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Scheme

    KAUST Repository

    Woźniak, M.

    2016-06-02

    We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.

  3. Inhomogeneous ordered states and translational nature of the gauge group in the Landau continuum theory: II. Applications of the general theory

    International Nuclear Information System (INIS)

    Braginsky, A. Ya.

    2007-01-01

    A group theory approach to description of phase transitions to an inhomogeneous ordered state, proposed in the preceding paper, is applied to two problems. First, a theory of the state of a liquid-crystalline smectic type-A phase under the action of uniaxial pressure is developed. Second, a model of strengthening in quasicrystals is constructed. According to the proposed approach, the so-called elastic dislocations always appear during the phase transitions in an inhomogeneous deformed state in addition to static dislocations, which are caused by peculiarities of the crystal growth or by other features in the prehistory of a sample. The density of static dislocations weakly depends on the external factors, whereas the density of elastic dislocations depends on the state. An analogy between the proposed theory of the inhomogeneous ordered state and the quantum-field theory of interaction between material fields is considered. On this basis, the phenomenological Ginzburg-Landau equation for the superconducting state is derived using the principle of locality of the transformation properties of the superconducting order parameter with respect to temporal translations

  4. Effect of Landau damping on kinetic Alfven and ion-acoustic solitary waves in a magnetized nonthermal plasma with warm ions

    International Nuclear Information System (INIS)

    Bandyopadhyay, Anup; Das, K.P.

    2002-01-01

    The evolution equations describing both kinetic Alfven wave and ion-acoustic wave in a nonthermal magnetized plasma with warm ions including weak nonlinearity and weak dispersion with the effect of Landau damping have been derived. These equations reduce to two coupled equations constituting the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation for both kinetic Alfven wave and ion-acoustic wave, including an extra term accounting for the effect of Landau damping. When the coefficient of the nonlinear term of the evolution equation for ion-acoustic wave vanishes, the nonlinear behavior of ion-acoustic wave, including the effect of Landau damping, is described by two coupled equations constituting the modified KdV-ZK (MKdV-ZK) equation, including an extra term accounting for the effect of Landau damping. It is found that there is no effect of Landau damping on the solitary structures of the kinetic Alfven wave. Both the macroscopic evolution equations for the ion-acoustic wave admits solitary wave solutions, the former having a sech 2 profile and the latter having a sech profile. In either case, it is found that the amplitude of the ion-acoustic solitary wave decreases slowly with time

  5. Shift of the superconducting critical parameters due to correlated disorder

    International Nuclear Information System (INIS)

    Gitterman, M.; Shapiro, I.; Shapiro, B.Ya.

    2012-01-01

    Shift of the critical temperature and second critical magnetic field are calculated for a superconductor with Gaussian correlated disorder. All calculations have been performed in the framework of the stochastic Ginzburg-Landau equation. For uncorrelated disorder the macroscopic critical temperature is determined by the average of the local critical temperature across the sample, while for correlated disorder both the critical temperature and the upper critical magnetic field depend on disorder correlation length. In a nonuniform superconductor with randomly distributed local critical temperature both the macroscopic critical temperature and the upper critical magnetic field strongly depend on the characteristic correlation length ρ 0 of correlated disorder. The shift of the macroscopic critical parameters from those for non-correlated disorder, which does not exist for white noise, is obtained for small ρ 0 in the framework of the Ginzburg-Landau theory.

  6. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

    Science.gov (United States)

    Murase, Kenya

    2015-01-01

    In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

  7. Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, Lennart; García-Morales, Vladimir [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching (Germany); Schönleber, Konrad; Krischer, Katharina, E-mail: krischer@tum.de [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)

    2014-03-15

    We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.

  8. Effects of periodic scattering potential on Landau quantization and ballistic transport of electrons in graphene

    Energy Technology Data Exchange (ETDEWEB)

    Gumbs, Godfrey [Department of Physics and Astronomy, Hunter College, CUNY, 695 Park Avenue, New York, NY 10065, USA and Donostia International Physics Center (DIPC), P de Manuel Lardizabal, 4, 20018 San Sebastian, Basque Country (Spain); Iurov, Andrii [Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, NY 10065 (United States); Huang, Danhong [Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, NM 87117 (United States); Fekete, Paula [West Point Military Academy, West Point, NY (United States); Zhemchuzhna, Liubov [Department of Physics, North Carolina Central University, Durham, North Carolina 27707 (United States)

    2014-03-31

    A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved numerically to display the structure of split Landau subbands as functions of both wave number and magnetic flux. The effects of pseudo-spin coupling and Landau subbands mixing by a strong scattering potential have been demonstrated. Additionally, we investigated the square barrier tunneling problem when magnetic field is present, as well as demonstrate the crucial difference in the modulated band structure between graphene and the two-dimensional electron gas. The low-magnetic field regime is particularly interesting for Dirac fermions and has been discussed. Tunneling of Dirac electrons through a magnetic potential barrier has been investigated to complement the reported results on electrostatic potential scattering in the presence of an ambient magnetic field.

  9. Effects of periodic scattering potential on Landau quantization and ballistic transport of electrons in graphene

    International Nuclear Information System (INIS)

    Gumbs, Godfrey; Iurov, Andrii; Huang, Danhong; Fekete, Paula; Zhemchuzhna, Liubov

    2014-01-01

    A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved numerically to display the structure of split Landau subbands as functions of both wave number and magnetic flux. The effects of pseudo-spin coupling and Landau subbands mixing by a strong scattering potential have been demonstrated. Additionally, we investigated the square barrier tunneling problem when magnetic field is present, as well as demonstrate the crucial difference in the modulated band structure between graphene and the two-dimensional electron gas. The low-magnetic field regime is particularly interesting for Dirac fermions and has been discussed. Tunneling of Dirac electrons through a magnetic potential barrier has been investigated to complement the reported results on electrostatic potential scattering in the presence of an ambient magnetic field

  10. Solving the Schroedinger equation using Smolyak interpolants

    International Nuclear Information System (INIS)

    Avila, Gustavo; Carrington, Tucker Jr.

    2013-01-01

    In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased

  11. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  12. Moving boundary - Oxygen diffusion. Two algorithms using Landau transformation

    International Nuclear Information System (INIS)

    Moyano, E.A.

    1991-01-01

    A description is made of two algorithms which solve a mathematical model destinated for the study of one-dimensional problems with moving boundaries and implicit boundary conditions. The Landau transformation is used in both methods for each temporal level so as to work all through with the same amount of nodes. Thus, it is necessary to deal with a partial differential equation whose diffusive and convective terms are accompanied by variable coefficients. The partial differential equation is made discrete implicitly, using the Laasonen scheme -which is always stable- instead of the Crank-Nicholson scheme, as performed by Ferris and Hill (5), in the fixed time passing method. The second method employs the tridiagonal algorithm. The first algorithm uses fixed time passing and iterates with variable interface positions, that is to say, it varies δs until it satisfies the boundary condition. The mathematical model describes oxygen diffusion in live tissues. Its numerical solution is obtained by finite differences. An important application of this method could be the estimation of the radiation dose in cancerous tumor treatment. (Author) [es

  13. Experimental quantum computing to solve systems of linear equations.

    Science.gov (United States)

    Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

    2013-06-07

    Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

  14. Calculation of strained BaTiO3 with different exchange correlation functionals examined with criterion by Ginzburg-Landau theory, uncovering expressions by crystallographic parameters

    Science.gov (United States)

    Watanabe, Yukio

    2018-05-01

    In the calculations of tetragonal BaTiO3, some exchange-correlation (XC) energy functionals such as local density approximation (LDA) have shown good agreement with experiments at room temperature (RT), e.g., spontaneous polarization (PS), and superiority compared with other XC functionals. This is due to the error compensation of the RT effect and, hence, will be ineffective in the heavily strained case such as domain boundaries. Here, ferroelectrics under large strain at RT are approximated as those at 0 K because the strain effect surpasses the RT effects. To find effective XC energy functionals for strained BaTiO3, we propose a new comparison, i.e., a criterion. This criterion is the properties at 0 K given by the Ginzburg-Landau (GL) theory because GL theory is a thermodynamic description of experiments working under the same symmetry-constraints as ab initio calculations. With this criterion, we examine LDA, generalized gradient approximations (GGA), meta-GGA, meta-GGA + local correlation potential (U), and hybrid functionals, which reveals the high accuracy of some XC functionals superior to XC functionals that have been regarded as accurate. This result is examined directly by the calculations of homogenously strained tetragonal BaTiO3, confirming the validity of the new criterion. In addition, the data points of theoretical PS vs. certain crystallographic parameters calculated with different XC functionals are found to lie on a single curve, despite their wide variations. Regarding these theoretical data points as corresponding to the experimental results, analytical expressions of the local PS using crystallographic parameters are uncovered. These expressions show the primary origin of BaTiO3 ferroelectricity as oxygen displacements. Elastic compliance and electrostrictive coefficients are estimated. For the comparison of strained results, we show that the effective critical temperature TC under strain 1000 K from an approximate method combining ab initio

  15. Method of mechanical quadratures for solving singular integral equations of various types

    Science.gov (United States)

    Sahakyan, A. V.; Amirjanyan, H. A.

    2018-04-01

    The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

  16. Fermion-induced quantum critical points

    OpenAIRE

    Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

    2017-01-01

    A unified theory of quantum critical points beyond the conventional Landau?Ginzburg?Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau?Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such t...

  17. Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems

    Directory of Open Access Journals (Sweden)

    Ahmad Makki

    2015-01-01

    Full Text Available Our aim is to prove the existence and uniqueness of solutions for one-dimensional Cahn-Hilliard and Allen-Cahn type equations based on a modification of the Ginzburg-Landau free energy proposed in [8]. In particular, the free energy contains an additional term called Willmore regularization and takes into account strong anisotropy effects.

  18. Origin of the Nonsinusoidal current-phase relation of a superconducting bridge

    International Nuclear Information System (INIS)

    Sugahara, M.

    1977-01-01

    The current-phase relation of a long superconducting bridge is investigated with the use of the Aslamazov-Larkin model and the Ginzburg-Landau equation. The feedback effect of the supercurrent to the phase difference in the weak link is taken into consideration. The derived nonsinusoidal current-phase relation explains the experiments of Jackel et al. very well

  19. Nodal spectrum method for solving neutron diffusion equation

    International Nuclear Information System (INIS)

    Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.

    1999-01-01

    Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations

  20. Solving the Schroedinger equation using the finite difference time domain method

    International Nuclear Information System (INIS)

    Sudiarta, I Wayan; Geldart, D J Wallace

    2007-01-01

    In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems

  1. Lagrange-Noether method for solving second-order differential equations

    Institute of Scientific and Technical Information of China (English)

    Wu Hui-Bin; Wu Run-Heng

    2009-01-01

    The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

  2. Landau-Ginzburg description of anomalous properties of novel room temperature multiferroics Pb(Fe{sub 1/2}Ta{sub 1/2}){sub x}(Zr{sub 0.53}Ti{sub 0.47}){sub 1-x}O{sub 3} and Pb(Fe{sub 1/2}Nb{sub 1/2}){sub x}(Zr{sub 0.53}Ti{sub 0.47}){sub 1−x}O{sub 3}

    Energy Technology Data Exchange (ETDEWEB)

    Glinchuk, Maya D.; Eliseev, Eugene A. [Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Krjijanovskogo 3, 03142 Kyiv (Ukraine); Morozovska, Anna N., E-mail: anna.n.morozovska@gmail.com [Institute of Physics, National Academy of Sciences of Ukraine, 46, pr. Nauky, 03028 Kyiv (Ukraine)

    2016-01-14

    Landau-Ginzburg thermodynamic formalism is used for the description of the anomalous ferroelectric, ferromagnetic, and magnetoelectric properties of Pb(Fe{sub 1/2}Ta{sub 1/2}){sub x}(Zr{sub 0.53}Ti{sub 0.47}){sub 1−x}O{sub 3} and Pb(Fe{sub 1/2}Nb{sub 1/2}){sub x}(Zr{sub 0.53}Ti{sub 0.47}){sub 1−x}O{sub 3} micro-ceramics. We calculated temperature, composition, and external field dependences of ferroelectric, ferromagnetic, and antiferromagnetic phases transition temperatures, remanent polarization, magnetization, hysteresis loops, dielectric permittivity, and magnetoelectric coupling. Special attention was paid to the comparison of developed theory with experiments. It appeared possible to describe adequately main experimental results including a reasonable agreement between the shape of calculated and measured hysteresis loops and remnant polarization. Since Landau-Ginzburg thermodynamic formalism appertains to single domain properties of a ferroic, we did not aim to describe quantitatively the coercive field under the presence of realistic poly-domain switching. Information about linear and nonlinear magnetoelectric coupling coefficients was extracted from the experimental data. From the fitting of experimental data with theoretical formula, we obtained the composition dependence of Curie-Weiss constant that is known to be inversely proportional to harmonic (linear) dielectric stiffness, as well as the strong nonlinear dependence of anharmonic parameters in free energy. Keeping in mind the essential influence of these parameters on multiferroic properties, the obtained results open the way to govern practically all the material properties with the help of suitable composition choice. A forecast of the strong enough influence of antiferrodistortive order parameter on the transition temperatures and so on the phase diagrams and properties of multiferroics are made on the basis of the developed theory.

  3. Multiparameter extrapolation and deflation methods for solving equation systems

    Directory of Open Access Journals (Sweden)

    A. J. Hughes Hallett

    1984-01-01

    Full Text Available Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.

  4. The order parameter equations of superfluid Fermi-liquid with spin-triplet pairing near Tc in magnetic field

    International Nuclear Information System (INIS)

    Tarasov, A.N.

    1995-01-01

    The article is devoted to description of equilibrium properties of superfluid phases of 3 He in magnetic field at temperatures near the normal-superfluid point T c . The Landau Fermi-liquid (F-L) approach generalized to superfluid Fermi-liquids (SFLs) is used. Equations for the order parameter paramagnetic SFL with spin-triplet pairing in static and uniform (DC) moderately strong magnetic field are derived without taking into account strong-coupling (SC) effects. An integro-differential equation is deduced for the order parameter in the general case of spin-triplet pairing (spin of a pair is s = 1, orbital moment l of a pair is any odd number). It is valid in the approximation of small space inhomogeneities of the SFL for external DC magnetic field at temperatures near T c . In the case of spin-triplet p-wave pairing a Ginzburg-Landau (GL) equation is derived for the order parameter A αj (complex 3 x 3 matrix). Corrections to the coefficients in the GL eq. are resulted from taking into account the influence of moderately strong DC magnetic field and spin-exchange F-L interaction by the theory of permutations. In such fields these corrections can be of the same order of magnitude as the so-called > SC corrections to the GL eq. (or even exceed them) and are much higher than the particle-hole asymmetric contribution. The above corrections are connected with deformation of the order parameter in moderate magnetic fields and are of interest at description of 3 He - B at low pressures

  5. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

    Science.gov (United States)

    Murase, Kenya

    2014-01-01

    Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

  6. Application of Monte Carlo method to solving boundary value problem of differential equations

    International Nuclear Information System (INIS)

    Zuo Yinghong; Wang Jianguo

    2012-01-01

    This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

  7. Two-dimensional quantisation of the quasi-Landau hydrogenic spectrum

    International Nuclear Information System (INIS)

    Gallas, J.A.C.; O'Connell, R.F.

    1982-01-01

    Based on the two-dimensional WKB model, an equation is derived from which the non-relativistic quasi-Landau energy spectrum of hydrogen-like atoms may be easily obtained. In addition, the solution of radial equations in the WKB approximation and its relation with models recently used to fit experimental data are discussed. (author)

  8. Ginzburg regime and its effects on topological defect formation

    International Nuclear Information System (INIS)

    Bettencourt, Luis M. A.; Antunes, Nuno D.; Zurek, W. H.

    2000-01-01

    The Ginzburg temperature has historically been proposed as the energy scale of formation of topological defects at a second order symmetry breaking phase transition. More recently alternative proposals which compute the time of formation of defects from the critical dynamics of the system have been gaining both theoretical and experimental support. We investigate, using a canonical model for string formation, how these two pictures compare. In particular we show that prolonged exposure of a critical field configuration to the Ginzburg regime results in no substantial suppression of the final density of defects formed. These results eliminate the Ginzburg regime as a possible cause of erasure of vortex lines in the recent 4 He pressure quench experiments. (c) 2000 The American Physical Society

  9. Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

    Energy Technology Data Exchange (ETDEWEB)

    Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence RI 02912 (United States)

    2016-03-14

    We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

  10. Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory

    International Nuclear Information System (INIS)

    Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

    2016-01-01

    We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

  11. Solving differential–algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas

    2006-01-01

    of a number of differential equations and algebraic equations — a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of ordinary differential equations — ODEs....

  12. Solving the Helmholtz equation in conformal mapped ARROWstructures using homotopy perturbation method

    DEFF Research Database (Denmark)

    Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole

    2011-01-01

    . The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution......The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method...

  13. Modified Chebyshev Collocation Method for Solving Differential Equations

    Directory of Open Access Journals (Sweden)

    M Ziaul Arif

    2015-05-01

    Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

  14. Possibility of Landau damping of gravitational waves

    International Nuclear Information System (INIS)

    Gayer, S.; Kennel, C.F.

    1979-01-01

    There is considerable uncertainty in the literature concerning whether or not transverse traceless gravitational waves can Landau damp. Physically, the issue is whether particles of nonzero mass can comove with surfaces of constant wave phase, and therefore, loosely, whether gravitational waves can have phase speeds less than that of light. We approach the question of Landau damping in various ways. We consider first the propagation of small-amplitude gravitational waves in an ideal fluid-filled Robertson-Walker universe of zero spatial curvature. We argue that the principle of equivalence requires those modes to be lightlike. We show that a freely moving particle interacting only with the collective fields cannot comove with such waves if it has nonzero mass. The equation for gravitational waves in collisionless kinetic gases differs from that for fluid media only by terms so small that deviations from lightlike propagation are unmeasurable. Thus, we conclude that Landau damping of small-amplitude, transverse traceless gravitational waves is not possible

  15. Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

    International Nuclear Information System (INIS)

    Ka-Lin, Su; Yuan-Xi, Xie

    2010-01-01

    By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)

  16. Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.

    Science.gov (United States)

    Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre

    2014-12-14

    We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

  17. Fibonacci-regularization method for solving Cauchy integral equations of the first kind

    Directory of Open Access Journals (Sweden)

    Mohammad Ali Fariborzi Araghi

    2017-09-01

    Full Text Available In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.

  18. Solving differential-algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph

    2006-01-01

    of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....

  19. Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

    Directory of Open Access Journals (Sweden)

    Thomas Gomez

    2018-04-01

    Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

  20. Thermal coupling effect on the vortex dynamics of superconducting thin films: time-dependent Ginzburg–Landau simulations

    Science.gov (United States)

    Jing, Ze; Yong, Huadong; Zhou, Youhe

    2018-05-01

    In this paper, vortex dynamics of superconducting thin films are numerically investigated by the generalized time-dependent Ginzburg–Landau (TDGL) theory. Interactions between vortex motion and the motion induced energy dissipation is considered by solving the coupled TDGL equation and the heat diffusion equation. It is found that thermal coupling has significant effects on the vortex dynamics of superconducting thin films. Branching in the vortex penetration path originates from the coupling between vortex motion and the motion induced energy dissipation. In addition, the environment temperature, the magnetic field ramp rate and the geometry of the superconducting film also greatly influence the vortex dynamic behaviors. Our results provide new insights into the dynamics of superconducting vortices, and give a mesoscopic understanding on the channeling and branching of vortex penetration paths during flux avalanches.

  1. Solving the Richardson equations close to the critical points

    Energy Technology Data Exchange (ETDEWEB)

    DomInguez, F [Departamento de Matematicas, Universidad de Alcala, 28871 Alcala de Henares (Spain); Esebbag, C [Departamento de Matematicas, Universidad de Alcala, 28871 Alcala de Henares (Spain); Dukelsky, J [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain)

    2006-09-15

    We study the Richardson equations close to the critical values of the pairing strength g{sub c}, where the occurrence of divergences precludes numerical solutions. We derive a set of equations for determining the critical g values and the non-collapsing pair energies. Studying the behaviour of the solutions close to the critical points, we develop a procedure to solve numerically the Richardson equations for arbitrary coupling strength.

  2. A Landau fluid model for dissipative trapped electron modes

    International Nuclear Information System (INIS)

    Hedrick, C.L.; Leboeuf, J.N.; Sidikman, K.L.

    1995-09-01

    A Landau fluid model for dissipative trapped electron modes is developed which focuses on an improved description of the ion dynamics. The model is simple enough to allow nonlinear calculations with many harmonics for the times necessary to reach saturation. The model is motivated by a discussion that starts with the gyro-kinetic equation and emphasizes the importance of simultaneously including particular features of magnetic drift resonance, shear, and Landau effects. To ensure that these features are simultaneously incorporated in a Landau fluid model with only two evolution equations, a new approach to determining the closure coefficients is employed. The effect of this technique is to reduce the matching of fluid and kinetic responses to a single variable, rather than two, and to allow focusing on essential features of the fluctuations in question, rather than features that are only important for other types of fluctuations. Radially resolved nonlinear calculations of this model, advanced in time to reach saturation, are presented to partially illustrate its intended use. These calculations have a large number of poloidal and toroidal harmonics to represent the nonlinear dynamics in a converged steady state which includes cascading of energy to both short and long wavelengths

  3. Ten-Year-Old Students Solving Linear Equations

    Science.gov (United States)

    Brizuela, Barbara; Schliemann, Analucia

    2004-01-01

    In this article, the authors seek to re-conceptualize the perspective regarding students' difficulties with algebra. While acknowledging that students "do" have difficulties when learning algebra, they also argue that the generally espoused criteria for algebra as the ability to work with the syntactical rules for solving equations is…

  4. students' preference of method of solving simultaneous equations

    African Journals Online (AJOL)

    Ugboduma,Samuel.O.

    substitution method irrespective of their gender for solving simultaneous equations. A recommendation ... advantage given to one method over others. Students' interest .... from two (2) single girls' schools, two (2) single boys schools and ten.

  5. Students' errors in solving linear equation word problems: Case ...

    African Journals Online (AJOL)

    The study examined errors students make in solving linear equation word problems with a view to expose the nature of these errors and to make suggestions for classroom teaching. A diagnostic test comprising 10 linear equation word problems, was administered to a sample (n=130) of senior high school first year Home ...

  6. Matrix factorizations and homological mirror symmetry on the torus

    International Nuclear Information System (INIS)

    Knapp, Johanna; Omer, Harun

    2007-01-01

    We consider matrix factorizations and homological mirror symmetry on the torus T 2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model

  7. Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations

    Directory of Open Access Journals (Sweden)

    Dequan Shang

    2013-01-01

    Full Text Available A predictor-corrector algorithm and an improved predictor-corrector (IPC algorithm based on Adams method are proposed to solve first-order differential equations with fuzzy initial condition. These algorithms are generated by updating the Adams predictor-corrector method and their convergence is also analyzed. Finally, the proposed methods are illustrated by solving an example.

  8. The Use of Transformations in Solving Equations

    Science.gov (United States)

    Libeskind, Shlomo

    2010-01-01

    Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…

  9. Final report [on solving the multigroup diffusion equations

    International Nuclear Information System (INIS)

    Birkhoff, G.

    1975-01-01

    Progress achieved in the development of variational methods for solving the multigroup neutron diffusion equations is described. An appraisal is made of the extent to which improved variational methods could advantageously replace difference methods currently used

  10. On method of solving third-order ordinary differential equations directly using Bernstein polynomials

    Science.gov (United States)

    Khataybeh, S. N.; Hashim, I.

    2018-04-01

    In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

  11. Semiconductor device simulation by a new method of solving poisson, Laplace and Schrodinger equations

    International Nuclear Information System (INIS)

    Sharifi, M. J.; Adibi, A.

    2000-01-01

    In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as poisson, Laplace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in several cases including the problem of finding electron concentration profile in the channel of a HEMT. In another section, we solve the Poisson equation by this method, choosing the problem of SBD as an example. Finally we solve the Laplace equation in two dimensions and as an example, we focus on the VED. In this paper, we have shown that, the method can get stable and precise results in solving all of these problems. Also the programs which have been written based on this method become considerably faster, more clear, and more abstract

  12. Oscillatory magneto-convection under magnetic field modulation

    Directory of Open Access Journals (Sweden)

    Palle Kiran

    2018-03-01

    Full Text Available In this paper we investigate an oscillatory mode of nonlinear magneto-convection under time dependant magnetic field. The time dependant magnetic field consists steady and oscillatory parts. The oscillatory part of the imposed magnetic field is assumed to be of third order. An externally imposed vertical magnetic field in an electrically conducting horizontal fluid layer is considered. The finite amplitude analysis is discussed while perturbing the system. The complex Ginzburg-Landau model is used to derive an amplitude of oscillatory convection for weakly nonlinear mode. Heat transfer is quantified in terms of the Nusselt number, which is governed by the Landau equation. The variation of the modulation excitation of the magnetic field alternates heat transfer in the layer. The modulation excitation of the magnetic field is used either to enhance or diminish the heat transfer in the system. Further, it is found that, oscillatory mode of convection enhances the heat transfer and than stationary convection. The results have possible technological applications in magnetic fluid based systems involving energy transmission. Keywords: Weakly nonlinear theory, Oscillatory convection, Complex Ginzburg Landau model, Magnetic modulation

  13. A method for solving neutron transport equation

    International Nuclear Information System (INIS)

    Dimitrijevic, Z.

    1993-01-01

    The procedure for solving the transport equation by directly integrating for case one-dimensional uniform multigroup medium is shown. The solution is expressed in terms of linear combination of function H n (x,μ), and the coefficient is determined from given conditions. The solution is applied for homogeneous slab of critical thickness. (author)

  14. Integral transform method for solving time fractional systems and fractional heat equation

    Directory of Open Access Journals (Sweden)

    Arman Aghili

    2014-01-01

    Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

  15. Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

    KAUST Repository

    Southern, J.A.

    2009-10-01

    The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

  16. Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

    KAUST Repository

    Southern, J.A.; Plank, G.; Vigmond, E.J.; Whiteley, J.P.

    2009-01-01

    The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

  17. Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics

    International Nuclear Information System (INIS)

    Passot, T.; Sulem, P. L.

    2005-01-01

    In may astrophysical plasmas such as the solar wind, the terrestrial magnetosphere, or in the interstellar medium at small enough scales, collisions are negligible. When interested in the large-scale dynamics, a hydrodynamic approach is advantageous not only because its numerical simulations is easier than of the full Vlasov-Maxwell equations, but also because it provides a deep understanding of cross-scale nonlinear couplings. It is thus of great interest to construct fluid models that extended the classical magnetohydrodynamic (MHD) equations to collisionless situations. Two ingredients need to be included in such a model to capture the main kinetic effects: finite Larmor radius (FLR) corrections and Landau damping, the only fluid-particle resonance that can affect large scales and can be modeled in a relatively simple way. The Modelization of Landau damping in a fluid formalism is hardly possible in the framework of a systematic asymptotic expansion and was addressed mainly by means of parameter fitting in a linearized setting. We introduced a similar Landau fluid model but, that has the advantage of taking dispersive effects into account. This model properly describes dispersive MHD waves in quasi-parallel propagation. Since, by construction, the system correctly reproduces their linear dynamics, appropriate tests should address the nonlinear regime. In a first case, we show analytically that the weakly nonlinear modulational dynamics of quasi-parallel propagating Alfven waves is well captured. As a second test we consider the parametric decay instability of parallel Alfven waves and show that numerical simulations of the dispersive Landau fluid model lead to results that closely match the outcome of hybrid simulations. (Author)

  18. GPU-advanced 3D electromagnetic simulations of superconductors in the Ginzburg–Landau formalism

    Energy Technology Data Exchange (ETDEWEB)

    Stošić, Darko; Stošić, Dušan; Ludermir, Teresa [Centro de Informática, Universidade Federal de Pernambuco, Av. Luiz Freire s/n, 50670-901, Recife, PE (Brazil); Stošić, Borko [Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irmãos, 52171-900 Recife, PE (Brazil); Milošević, Milorad V., E-mail: milorad.milosevic@uantwerpen.be [Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium)

    2016-10-01

    Ginzburg–Landau theory is one of the most powerful phenomenological theories in physics, with particular predictive value in superconductivity. The formalism solves coupled nonlinear differential equations for both the electronic and magnetic responsiveness of a given superconductor to external electromagnetic excitations. With order parameter varying on the short scale of the coherence length, and the magnetic field being long-range, the numerical handling of 3D simulations becomes extremely challenging and time-consuming for realistic samples. Here we show precisely how one can employ graphics-processing units (GPUs) for this type of calculations, and obtain physics answers of interest in a reasonable time-frame – with speedup of over 100× compared to best available CPU implementations of the theory on a 256{sup 3} grid.

  19. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

    Science.gov (United States)

    Murase, Kenya

    2016-01-01

    In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

  20. Approximate analytical methods for solving ordinary differential equations

    CERN Document Server

    Radhika, TSL; Rani, T Raja

    2015-01-01

    Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti

  1. Confinement of monopole field lines in a superconductor at T ≠ 0

    International Nuclear Information System (INIS)

    Cardoso, Marco; Bicudo, Pedro; Sacramento, Pedro D.

    2008-01-01

    We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity

  2. Condensate localization by mesoscale disorder in high-Tc superconductors

    International Nuclear Information System (INIS)

    Kumar, N.

    1994-06-01

    We propose and solve approximately a phenomenological model for Anderson localization of the macroscopic wavefunction for an inhomogeneous superconductor quench-disordered on the mesoscale of the order of the coherence length ξ 0 . Our treatment is based on the non-linear Schroedinger equation resulting from the Ginzburg-Landau free-energy functional having a spatially random coefficient representing spatial disorder of the pairing interaction. Linearization of the equation, valid close to the critical temperature T c , or to the upper critical field H c2 (T c ) maps it to the Anderson localization problem with T c identified with the mobility edge. For the highly anisotropic high-T c materials and thin (2D) films in the quantum Hall geometry, we predict windows of re-entrant superconductivity centered at integrally spaced temperature values. Our model treatment also provides a possible explanation for the critical current J c perpendicular becoming non-zero on cooling before J c parallel does in some high-T c superconductors. (author). 18 refs

  3. Nonlinearly Activated Neural Network for Solving Time-Varying Complex Sylvester Equation.

    Science.gov (United States)

    Li, Shuai; Li, Yangming

    2013-10-28

    The Sylvester equation is often encountered in mathematics and control theory. For the general time-invariant Sylvester equation problem, which is defined in the domain of complex numbers, the Bartels-Stewart algorithm and its extensions are effective and widely used with an O(n³) time complexity. When applied to solving the time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. For the special case of the general Sylvester equation problem defined in the domain of real numbers, gradient-based recurrent neural networks are able to solve the time-varying Sylvester equation in real time, but there always exists an estimation error while a recently proposed recurrent neural network by Zhang et al [this type of neural network is called Zhang neural network (ZNN)] converges to the solution ideally. The advancements in complex-valued neural networks cast light to extend the existing real-valued ZNN for solving the time-varying real-valued Sylvester equation to its counterpart in the domain of complex numbers. In this paper, a complex-valued ZNN for solving the complex-valued Sylvester equation problem is investigated and the global convergence of the neural network is proven with the proposed nonlinear complex-valued activation functions. Moreover, a special type of activation function with a core function, called sign-bi-power function, is proven to enable the ZNN to converge in finite time, which further enhances its advantage in online processing. In this case, the upper bound of the convergence time is also derived analytically. Simulations are performed to evaluate and compare the performance of the neural network with different parameters and activation functions. Both theoretical analysis and numerical simulations validate the effectiveness of the proposed method.

  4. Reversible dissipative processes, conformal motions and Landau damping

    International Nuclear Information System (INIS)

    Herrera, L.; Di Prisco, A.; Ibáñez, J.

    2012-01-01

    The existence of a dissipative flux vector is known to be compatible with reversible processes, provided a timelike conformal Killing vector (CKV) χ α =(V α )/T (where V α and T denote the four-velocity and temperature respectively) is admitted by the spacetime. Here we show that if a constitutive transport equation, either within the context of standard irreversible thermodynamics or the causal Israel–Stewart theory, is adopted, then such a compatibility also requires vanishing dissipative fluxes. Therefore, in this later case the vanishing of entropy production generated by the existence of such CKV is not actually associated to an imperfect fluid, but to a non-dissipative one. We discuss also about Landau damping. -- Highlights: ► We review the problem of compatibility of dissipation with reversibility. ► We show that the additional assumption of a transport equation renders such a compatibility trivial. ► We discuss about Landau damping.

  5. Gyro-Landau fluid model of tokamak core fluctuations

    International Nuclear Information System (INIS)

    Leboeuf, J.N.; Carreras, B.A.; Dominguez, N.; Hedrick, C.L.; Sidikman, K.L.; Lynch, V.E.; Drake, J.B.; Walker, D.W.

    1992-01-01

    Dissipative trapped electron modes (DTEM) may be one of the causes of deterioration of confinement in tokamak and stellatator plasmas. We have implemented a fluid model to study DTEM turbulence in slab geometry. The electron dynamics include in addition to the adiabatic part, a non-adiabatic piece modeled with an i-delta-type response. The ion dynamics include Landau damping and FLR corrections through Landau fluid approximate techniques and Pade approximants for Γ 0 (b)=I 0 (b)e -b . The model follows from the gyrokinetic equation. Evolution equations, which closely resemble those used in standard reduced MHD, are presented since these are better suited to non-linear calculations. The numerical results of radially resolved calculations will be discussed. A recently developed hybrid model, which consists of a gyrokinetic implementation for the ions using particles and the same description for the electron dynamics as in the fluid model, will also be presented

  6. Reversible dissipative processes, conformal motions and Landau damping

    Energy Technology Data Exchange (ETDEWEB)

    Herrera, L., E-mail: laherrera@cantv.net.ve [Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco, Bilbao (Spain); Di Prisco, A., E-mail: adiprisc@fisica.ciens.ucv.ve [Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco, Bilbao (Spain); Ibáñez, J., E-mail: j.ibanez@ehu.es [Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco, Bilbao (Spain)

    2012-02-06

    The existence of a dissipative flux vector is known to be compatible with reversible processes, provided a timelike conformal Killing vector (CKV) χ{sup α}=(V{sup α})/T (where V{sup α} and T denote the four-velocity and temperature respectively) is admitted by the spacetime. Here we show that if a constitutive transport equation, either within the context of standard irreversible thermodynamics or the causal Israel–Stewart theory, is adopted, then such a compatibility also requires vanishing dissipative fluxes. Therefore, in this later case the vanishing of entropy production generated by the existence of such CKV is not actually associated to an imperfect fluid, but to a non-dissipative one. We discuss also about Landau damping. -- Highlights: ► We review the problem of compatibility of dissipation with reversibility. ► We show that the additional assumption of a transport equation renders such a compatibility trivial. ► We discuss about Landau damping.

  7. Equilibrium properties of proximity effect

    International Nuclear Information System (INIS)

    Esteve, D.; Pothier, H.; Gueron, S.; Birge, N.O.; Devoret, M.

    1996-01-01

    The proximity effect in diffusive normal-superconducting (NS) nano-structures is described by the Usadel equations for the electron pair correlations. We show that these equations obey a variational principle with a potential which generalizes the Ginzburg-Landau energy functional. We discuss simple examples of NS circuits using this formalism. In order to test the theoretical predictions of the Usadel equations, we have measured the density of states as a function of energy on a long N wire in contact with a S wire at one end, at different distances from the NS interface. (authors)

  8. Normal scheme for solving the transport equation independently of spatial discretization

    International Nuclear Information System (INIS)

    Zamonsky, O.M.

    1993-01-01

    To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)

  9. Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate

    International Nuclear Information System (INIS)

    Guilleumas, M.; Pitaevskii, L.P.

    2003-01-01

    We have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed

  10. Birationality and Landau-Ginzburg Models

    Science.gov (United States)

    Clarke, Patrick

    2017-08-01

    We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev-Nill (Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, volume 452 of Contemporary mathematics. American Mathematical Society, Providence, pp 35-66, 2008) about the birationality of Calabi-Yau families associated to multiple mirror nef-partitions. This completes the progress in this direction made by Li's breakthrough (Li in Adv Math 299:71-107, 2016). In the process, we obtain results in the theory of Borisov's nef-partitions (Borisov in Towards the mirror symmetry for Calabi-Yau complete intersections in Gorenstein toric Fano varieties, 1993. arXiv:alg-geom/9310001 ) and provide new insight into the geometric content of the multiple mirror phenomenon.

  11. A quark-antiquark potential from a superconducting model of confinement

    Directory of Open Access Journals (Sweden)

    J.W. Alcock

    1983-10-01

    Full Text Available The Landau-Ginzburg phenomenological theory of superconductivity is used as a model of flux confinement. A monopole pair of sources is included to simulate a quark-antiquark system. The interaction energy is found in the static approximation appropriate for heavy quark systems, and equated with the interquark potential. This potential is compared with other suggested phenomenological potentials and succeeds in reproducing heavy quark spectra.

  12. Rigorous study of the gap equation for an inhomogeneous superconducting state near T/sub c/

    International Nuclear Information System (INIS)

    Hu, C.

    1975-01-01

    A rigorous analytic study of the self-consistent gap equation (symobolically Δ=F/sub T/Δ), for an inhomogeneous superconducting state, is presented in the Bogoliubov formulation. The gap function Δ (r) is taken to simulate a planar normal-superconducting phase boundary: Δ (r) =Δ/sub infinity/ tanh(αΔ/sub infinity/z/v/sub F/) THETA (z), where Δ/sub infinity/(T) is the equilibrium gap, v/subF/ is the Fermi velocity, and THETA (z) is a unit step function. First a special space integral of the gap equation proportional∫ 0 /sub +//sup infinity/(F/sub T/-Δ)(dΔ/dz) dz is evaluated essentially exactly, except for a nonperturbative WKBJ approximation used in solving the Bogoliubov--de Gennes equations. It is then expanded near the transition temperature T/sub c/ in power of Δ/sub infinity/proportional (1-T/T/sub c/) 1 / 2 , demonstrating an exact cancellation of a subseries of ''anomalous-order'' terms. The leading surviving term is found to agree in order, but not in magnitude, with the Ginzburg-Landau-Gor'kov (GLG) approximation. The discrepancy is found to be linked to the slope discontinuity in our chosen Δ. A contour-integral technique in a complex-energy plane is then devised to evaluate the local value of F/sub T/-Δ exactly. Our result reveals that near T/sub c/ this method can reproduce the GLG result essentially everywhere, except within a BCS coherence length not xi (T) exclamation from a singularity in Δ, where F/sub T/-Δ can have a singular contribution with an ''anomalous'' local magnitude, not expected from the GLG approach. This anomalous term precisely accounts for the discrepancy found in the special integral of the gap equation as mentioned above, and likely explains the ultimate origin of the anomalous terms found in the free energy of an isolated vortex line by Cleary

  13. Sufficient Descent Conjugate Gradient Methods for Solving Convex Constrained Nonlinear Monotone Equations

    Directory of Open Access Journals (Sweden)

    San-Yang Liu

    2014-01-01

    Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.

  14. Solving the interval type-2 fuzzy polynomial equation using the ranking method

    Science.gov (United States)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim

    2014-07-01

    Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

  15. A predictor-corrector scheme for solving the Volterra integral equation

    KAUST Repository

    Al Jarro, Ahmed

    2011-08-01

    The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.

  16. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

    Science.gov (United States)

    Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

    2013-01-01

    We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

  17. Fluctuating dynamics of nematic liquid crystals using the stochastic method of lines

    Science.gov (United States)

    Bhattacharjee, A. K.; Menon, Gautam I.; Adhikari, R.

    2010-07-01

    We construct Langevin equations describing the fluctuations of the tensor order parameter Qαβ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de Gennes free energy. The noise is required to preserve the symmetry and tracelessness of the tensor order parameter and must satisfy a fluctuation-dissipation relation at thermal equilibrium. We construct a noise with these properties in a basis of symmetric traceless matrices and show that the Langevin equations can be solved numerically in this basis using a stochastic version of the method of lines. The numerical method is validated by comparing equilibrium probability distributions, structure factors, and dynamic correlations obtained from these numerical solutions with analytic predictions. We demonstrate excellent agreement between numerics and theory. This methodology can be applied to the study of phenomena where fluctuations in both the magnitude and direction of nematic order are important, as for instance, in the nematic swarms which produce enhanced opalescence near the isotropic-nematic transition or the problem of nucleation of the nematic from the isotropic phase.

  18. A method of solving simple harmonic oscillator Schroedinger equation

    Science.gov (United States)

    Maury, Juan Carlos F.

    1995-01-01

    A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.

  19. Domain walls of BaTiO.sub.3./sub. and PbTiO.sub.3./sub. within Ginzburg-Landau-Devonshire model

    Czech Academy of Sciences Publication Activity Database

    Hlinka, Jiří

    2008-01-01

    Roč. 375, č. 1 (2008), 132-137 ISSN 0015-0193 R&D Projects: GA ČR GA202/06/0411 Institutional research plan: CEZ:AV0Z10100520 Keywords : domain walls * Landau- Ginsburg theory * ferroelectricity * BaTiO 3 * PbTiO 3 Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.562, year: 2008

  20. Using Computer Symbolic Algebra to Solve Differential Equations.

    Science.gov (United States)

    Mathews, John H.

    1989-01-01

    This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

  1. Will learning to solve one-step equations pose a challenge to 8th grade students?

    Science.gov (United States)

    Ngu, Bing Hiong; Phan, Huy P.

    2017-08-01

    Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. Element interactivity arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features (e.g. negative pronumeral) poses additional challenge to master equation solving skills. In an experiment, 41 8th grade students (girls = 16, boys = 25) sat for a pre-test, attended a session about equation solving, completed an acquisition phase which constituted the main intervention and were tested again in a post-test. The results showed that at post-test, students performed better on one-step equations tapping low rather than high element interactivity knowledge. In addition, students performed better on those one-step equations that contained no special features. Thus, both the degree of element interactivity and the operation with special features affect the challenge posed to 8th grade students on learning how to solve one-step equations.

  2. Stability analysis of cavity solitons governed by the cubic-quintic Ginzburg-Landau equation

    International Nuclear Information System (INIS)

    Ding, Edwin; Kutz, J Nathan; Luh, Kyle

    2011-01-01

    A theoretical model is proposed to describe the formation of two-dimensional solitons in a laser cavity, extending the concept of the mode locking of temporal solitons in fibre lasers to spatial mode locking in nonlinear crystals. A linear stability analysis of the governing model based upon radial symmetry is performed to characterize the multi-pulsing instability of the laser as a function of gain. It is found that a stable n-pulse solution of the system bifurcates into a (n + 1)-pulse solution through the development of a periodic solution (Hopf bifurcation), and the results are consistent with simulations of the full model.

  3. Solving Eigenvalue response matrix equations with Jacobian-Free Newton-Krylov methods

    International Nuclear Information System (INIS)

    Roberts, Jeremy A.; Forget, Benoit

    2011-01-01

    The response matrix method for reactor eigenvalue problems is motivated as a technique for solving coarse mesh transport equations, and the classical approach of power iteration (PI) for solution is described. The method is then reformulated as a nonlinear system of equations, and the associated Jacobian is derived. A Jacobian-Free Newton-Krylov (JFNK) method is employed to solve the system, using an approximate Jacobian coupled with incomplete factorization as a preconditioner. The unpreconditioned JFNK slightly outperforms PI, and preconditioned JFNK outperforms both PI and Steffensen-accelerated PI significantly. (author)

  4. Taylor's series method for solving the nonlinear point kinetics equations

    International Nuclear Information System (INIS)

    Nahla, Abdallah A.

    2011-01-01

    Highlights: → Taylor's series method for nonlinear point kinetics equations is applied. → The general order of derivatives are derived for this system. → Stability of Taylor's series method is studied. → Taylor's series method is A-stable for negative reactivity. → Taylor's series method is an accurate computational technique. - Abstract: Taylor's series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor's series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor's series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

  5. Aperiodic superconducting phase boundary of periodic micronetworks in a magnetic field

    International Nuclear Information System (INIS)

    Nori, F.; Niu, Q.

    1988-01-01

    We study flux quantization in periodic arrays with two elementary cells having an irrational ratio of areas. In particular, we calculate the superconducting-normal phase boundary T/sub c/(H) and we analyze the origin of its overall and fine structure as a function of the network size. We discuss our theoretical results, exploiting the electronic tight-binding analogy to the Ginzburg-Landau equations, and compare them with the experimental ones

  6. Field-theoretical description of itinerant spin glasses

    International Nuclear Information System (INIS)

    Kolley, E.; Kolley, W.

    1986-01-01

    By means of functional integral technique at T 0 the disordered Hubbard model is bosonized, resulting in an effective action of the Ginzburg-Landau type. The quenched-averaged free energy of the itinerant spin glass is calculated by using the replica trick and Bogolyubov's variational principle. The spinglass order parameter and the local magnetic moment fulfil a system of self-consistent equations in the presence of spatial fluctuations. (author)

  7. ELMy-H mode as limit cycle and chaotic oscillations in tokamak plasmas

    International Nuclear Information System (INIS)

    Itoh Sanae, I.; Itoh, Kimitaka; Fukuyama, Atsushi; Miura, Yukitoshi.

    1991-05-01

    A model of Edge Localized Modes (ELMs) in tokamak plasmas is presented. A limit cycle solution is found in the transport equation (time-dependent Ginzburg-Landau type), which a has hysteresis curve between the gradient and flux. Periodic oscillation of the particle outflux and L/H intermediate state are predicted near the L/H transition boundary. A mesophase in spatial structure appears near edge. Chaotic oscillation is also predicted. (author)

  8. Fermion-induced quantum critical points.

    Science.gov (United States)

    Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

    2017-08-22

    A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

  9. Matrix factorisations for rational boundary conditions by defect fusion

    International Nuclear Information System (INIS)

    Behr, Nicolas; Fredenhagen, Stefan

    2015-01-01

    A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.

  10. Matrix factorisations for rational boundary conditions by defect fusion

    Energy Technology Data Exchange (ETDEWEB)

    Behr, Nicolas [Department of Mathematics, Heriot-Watt University,Riccarton, Edinburgh, EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences,Edinburgh (United Kingdom); Fredenhagen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,D-14424 Golm (Germany)

    2015-05-11

    A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.

  11. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  12. Landau and modern physics

    International Nuclear Information System (INIS)

    Pokrovsky, Valery L

    2009-01-01

    This article describes the history of the creation and further development of Landau's famous works on phase transitions, diamagnetism of electron gas (Landau levels), and quantum transitions at a level crossing (the Landau-Zener phenomenon), and its role in modern physics. (methodological notes)

  13. Solving the discrete KdV equation with homotopy analysis method

    International Nuclear Information System (INIS)

    Zou, L.; Zong, Z.; Wang, Z.; He, L.

    2007-01-01

    In this Letter, we apply the homotopy analysis method to differential-difference equations. We take the discrete KdV equation as an example, and successfully obtain double periodic wave solutions and solitary wave solutions. It illustrates the validity and the great potential of the homotopy analysis method in solving discrete KdV equation. Comparisons are made between the results of the proposed method and exact solutions. The results reveal that the proposed method is very effective and convenient

  14. Decoherence and Landau-Damping

    Energy Technology Data Exchange (ETDEWEB)

    Ng, K.Y.; /Fermilab

    2005-12-01

    The terminologies, decoherence and Landau damping, are often used concerning the damping of a collective instability. This article revisits the difference and relation between decoherence and Landau damping. A model is given to demonstrate how Landau damping affects the rate of damping coming from decoherence.

  15. A Model for Solving the Maxwell Quasi Stationary Equations in a 3-Phase Electric Reduction Furnace

    Directory of Open Access Journals (Sweden)

    S. Ekrann

    1982-10-01

    Full Text Available A computer code has been developed for the approximate computation of electric and magnetic fields within an electric reduction furnace. The paper describes the numerical methods used to solve Maxwell's quasi-stationary equations, which are the governing equations for this problem. The equations are discretized by a staggered grid finite difference technique. The resulting algebraic equations are solved by iterating between computations of electric and magnetic quantities. This 'outer' iteration converges only when the skin depth is larger or of about the same magnitude as the linear dimensions of the computational domain. In solving for electric quantities with magnetic quantities being regarded as known, and vice versa, the central computational task is the solution of a Poisson equation for a scalar potential. These equations are solved by line successive overrelaxation combined with a rebalancing technique.

  16. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  17. Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

    International Nuclear Information System (INIS)

    Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

    2005-01-01

    In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

  18. Equilibrium properties of proximity effect

    Energy Technology Data Exchange (ETDEWEB)

    Esteve, D.; Pothier, H.; Gueron, S.; Birge, N.O.; Devoret, M.

    1996-12-31

    The proximity effect in diffusive normal-superconducting (NS) nano-structures is described by the Usadel equations for the electron pair correlations. We show that these equations obey a variational principle with a potential which generalizes the Ginzburg-Landau energy functional. We discuss simple examples of NS circuits using this formalism. In order to test the theoretical predictions of the Usadel equations, we have measured the density of states as a function of energy on a long N wire in contact with a S wire at one end, at different distances from the NS interface. (authors). 12 refs.

  19. A highly accurate method to solve Fisher's equation

    Indian Academy of Sciences (India)

    The solution of the Helmholtz equation was approximated by a sixth-order compact finite difference. (CFD6) method in [29]. In [30], a CFD6 scheme has been presented to ... efficiency of the proposed method are reported in §3. Finally .... our discussion, one can apply the proposed method to solve the more general problem.

  20. Dispersion relation and Landau damping of waves in high-energy density plasmas

    International Nuclear Information System (INIS)

    Zhu Jun; Ji Peiyong

    2012-01-01

    We present a theoretical investigation on the propagation of electromagnetic waves and electron plasma waves in high energy density plasmas using the covariant Wigner function approach. Based on the covariant Wigner function and Dirac equation, a relativistic quantum kinetic model is established to describe the physical processes in high-energy density plasmas. With the zero-temperature Fermi–Dirac distribution, the dispersion relation and Landau damping of waves containing the relativistic quantum corrected terms are derived. The relativistic quantum corrections to the dispersion relation and Landau damping are analyzed by comparing our results with those obtained in classical and non-relativistic quantum plasmas. We provide a detailed discussion on the Landau damping obtained in classical plasmas, non-relativistic Fermi plasmas and relativistic Fermi plasmas. The contributions of the Bohm potential, the Fermi statistics pressure and relativistic effects to the dispersion relation and Landau damping of waves are quantitatively calculated with real plasma parameters. (paper)

  1. Theory of Nernst effect in layered superconductors

    International Nuclear Information System (INIS)

    Tinh, B D; Rosenstein, B

    2009-01-01

    We calculate, using the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise, the transverse thermoelectric conductivity α xy , describing the Nernst effect, in type-II superconductor in the vortex-liquid regime. The method is an elaboration of the Hartree-Fock. An often made in analytical calculations additional assumption that only the lowest Landau level significantly contributes to α xy in the high field limit is lifted by including all the Landau levels. The resulting values in two dimensions (2D) are significantly lower than the numerical simulation data of the same model, but are in reasonably good quantitative agreement with experimental data on La 2 SrCuO 4 above the irreversibility line (below the irreversibility line at which α xy diverges and theory should be modified by including pinning effects).

  2. Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

    Science.gov (United States)

    Agarwal, P.; El-Sayed, A. A.

    2018-06-01

    In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

  3. New method for solving three-dimensional Schroedinger equation

    International Nuclear Information System (INIS)

    Melezhik, V.S.

    1990-01-01

    The method derived recently for solving a multidimensional scattering problem is applied to a three-dimensional Schroedinger equation. As compared with direct three-dimensional calculations of finite elements and finite differences, this approach gives sufficiently accurate upper and lower approximations to the helium-atom binding energy, which demonstrates its efficiency. 15 refs.; 1 fig.; 2 tabs

  4. Superconductor in a weak static gravitational field

    Energy Technology Data Exchange (ETDEWEB)

    Ummarino, Giovanni Alberto [Dipartimento DISAT, Politecnico di Torino, Turin (Italy); National Research Nuclear University MEPhI-Moscow Engineering Physics Institute, Moscow (Russian Federation); Gallerati, Antonio [Dipartimento DISAT, Politecnico di Torino, Turin (Italy)

    2017-08-15

    We provide the detailed calculation of a general form for Maxwell and London equations that takes into account gravitational corrections in linear approximation. We determine the possible alteration of a static gravitational field in a superconductor making use of the time-dependent Ginzburg-Landau equations, providing also an analytic solution in the weak field condition. Finally, we compare the behavior of a high-T{sub c} superconductor with a classical low-T{sub c} superconductor, analyzing the values of the parameters that can enhance the reduction of the gravitational field. (orig.)

  5. Forces and energy dissipation in inhomogeneous non-equilibrium superconductors

    International Nuclear Information System (INIS)

    Poluehktov, Yu.M.; Slezov, V.V.

    1987-01-01

    The phenomenological theory of volume forces and dissipation processes in inhomogeneous non-equilibrium superconductors near temperature transition from the normal to superconducting state is constructed. The approach is based on application of dynamic equations of superconductivity formulated on the basis of the Lagrangian formalism. These equations are generalized the Ginzburg-Landau theory in the nonstationary non-equilibrium case for ''foul'' superconductors. The value estimations of volume forces arising in inhomogeneities during relaxation of an order parameter and when the electrical field is penetrated into the superconductor, are given

  6. A neuro approach to solve fuzzy Riccati differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)

    2015-10-22

    There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

  7. A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation

    Directory of Open Access Journals (Sweden)

    Mingzhu Li

    2014-01-01

    Full Text Available The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.

  8. Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

    Directory of Open Access Journals (Sweden)

    Reza Mokhtari

    2012-01-01

    Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.

  9. Pattern formation and chaos in synergetic systems

    Energy Technology Data Exchange (ETDEWEB)

    Haken, H

    1985-01-01

    A general approach to the reduction of the equations of systems composed of many subsystems of equations for, in general, few order parameters at instability points is sketched. As special case generalized Ginzburg-Landau equations are obtained. Recent results based on these equations, showing pattern formation in the convection instability and flames, are presented. Bifurcations from tori to other tori are treated, and some general conclusions are drawn. Analogies between fluid dynamics and lasers which led to the prediction of laser light chaos by Haken (1975) are pointed out. Finally the suspension of a class of discrete one-dimensional maps is discussed and explicitly presented for a typical case. 21 references.

  10. A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

    Directory of Open Access Journals (Sweden)

    Inci Cilingir Sungu

    2015-01-01

    Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.

  11. Theoretical upper critical field Hc2 for inhomogeneous high temperature superconductors

    International Nuclear Information System (INIS)

    Caixeiro, E.S.; Gonzalez, J.L.; Mello, E.V.L. de

    2004-01-01

    We present the theoretical upper critical field H c2 (T) of the high temperature superconductors (HTSC), calculated through a linearized Ginzburg-Landau equation modified to consider the intrinsic inhomogeneity of the HTSC. The unusual behavior of H c2 (T) for these compounds, and other properties like the Meissner and Nernst effects detected at temperatures much higher than the critical temperature T c of the sample, are explained by the approach

  12. Superconductivity: Phenomenology

    International Nuclear Information System (INIS)

    Falicov, L.M.

    1988-08-01

    This document discusses first the following topics: (a) The superconducting transition temperature; (b) Zero resistivity; (c) The Meissner effect; (d) The isotope effect; (e) Microwave and optical properties; and (f) The superconducting energy gap. Part II of this document investigates the Ginzburg-Landau equations by discussing: (a) The coherence length; (b) The penetration depth; (c) Flux quantization; (d) Magnetic-field dependence of the energy gap; (e) Quantum interference phenomena; and (f) The Josephson effect

  13. Isotope decay equations solved by means of a recursive method

    International Nuclear Information System (INIS)

    Grant, Carlos

    2009-01-01

    The isotope decay equations have been solved using forward finite differences taking small time steps, among other methods. This is the case of the cell code WIMS, where it is assumed that concentrations of all fissionable isotopes remain constant during the integration interval among other simplifications. Even when the problem could be solved running through a logical tree, all algorithms used for resolution of these equations used an iterative programming formulation. That happened because nearly all computer languages used up to a recent past by the scientific programmers did not support recursion, such as the case of the old versions of FORTRAN or BASIC. Nowadays also an integral form of the depletion equations is used in Monte Carlo simulation. In this paper we propose another programming solution using a recursive algorithm, running through all descendants of each isotope and adding their contributions to all isotopes in each generation. The only assumption made for this solution is that fluxes remain constant during the whole time step. Recursive process is interrupted when a stable isotope was attained or the calculated contributions are smaller than a given precision. These algorithms can be solved by means an exact analytic method that can have some problems when circular loops appear for isotopes with alpha decay, and a more general polynomial method. Both methods are shown. (author)

  14. Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool

    Science.gov (United States)

    Sanchez Perez, J. F.; Conesa, M.; Alhama, I.

    2016-11-01

    Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.

  15. Vacuum Bloch-Siegert shift in Landau polaritons with ultra-high cooperativity

    Science.gov (United States)

    Li, Xinwei; Bamba, Motoaki; Zhang, Qi; Fallahi, Saeed; Gardner, Geoff C.; Gao, Weilu; Lou, Minhan; Yoshioka, Katsumasa; Manfra, Michael J.; Kono, Junichiro

    2018-06-01

    A two-level system resonantly interacting with an a.c. magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrödinger's equation for this seemingly simple system can be solved exactly only under the rotating-wave approximation, which neglects the counter-rotating field component. When the a.c. field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch-Siegert shift. Here, we report the vacuum Bloch-Siegert shift, which is induced by the ultra-strong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility two-dimensional electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum Bloch-Siegert shift up to 40 GHz. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field.

  16. Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

    International Nuclear Information System (INIS)

    Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.

    1996-01-01

    This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

  17. Weak and strong turbulence in the CGL equation

    International Nuclear Information System (INIS)

    Gibbon, J.D.; Bartuccelli, M.V.; Doering, C.R.

    1993-01-01

    To many fluid dynamicists, the only real turbulence is the fine scale 3-dimensional turbulence which occurs at high Reynolds numbers, with an energy cascade and an inertial subrange. The number of degrees of freedom in 3d strong turbulence is clearly many orders of magnitude greater than in such phenomena as convection in a box where perhaps only a few spatial modes govern the dynamics. Only in 2d are the incompressible Navier Stokes equations understood analytically in the sense that there is a rigorous proof of the existence of a finite dimensional global attractor. Computational methods are generally good enough to resolve the smallest scale in a 2d flow and, for 2d homogeneous decaying turbulence, the vorticity obeys a maximum principle. No such maximum principle is known to exist in 3d and regularity remains to be proved. Numerical resolution of the smallest scale in a fully turbulent 3d flow is still a long way off. In order to attempt to get a better grip on the tantalizing phenomena displayed by the Navier Stokes equations, it is a useful exercise to see whether it is possible to mimic some limited features of the 3d Navier Stokes equations with a different PDE system which displays similar functional properties but in a lower spatial dimension. This exercise, however, must obviously be limited by the fact that simpler models in lower dimensions cannot display the vortex stretching properties displayed by the 3d Navier Stokes equations, although the lowering of the spatial dimension does make it easier to compute the dynamics. One equation which will be shown to have some of the desired properites is a version of the d dimensional complex Ginzburg Landau (CDL) equation on the periodic domain [0,1]. It is not our intention here to treat it in its physical context. Our intention in using it is to try and mimic limited features of the Navier Stokes equations with an equation over which we have more analytical control

  18. Solving Nonlinear Partial Differential Equations with Maple and Mathematica

    CERN Document Server

    Shingareva, Inna K

    2011-01-01

    The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

  19. Solving nonlinear evolution equation system using two different methods

    Science.gov (United States)

    Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

    2015-12-01

    This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

  20. Effective methods of solving of model equations of certain class of thermal systems

    International Nuclear Information System (INIS)

    Lach, J.

    1985-01-01

    A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)

  1. Generalized Landau-Lifshitz-Gilbert equation for uniformly magnetized bodies

    Energy Technology Data Exchange (ETDEWEB)

    Serpico, C. [Dipartimento di Ingegneria Elettrica, Universita di Napoli ' FedericoII' , Via Claudio 21, I-80125 Naples (Italy)], E-mail: serpico@unina.it; Mayergoyz, I.D. [ECE Department and UMIACS, University of Maryland, College Park, MD 20742 (United States); Bertotti, G. [Istituto Nazionale di Ricerca Metrologica (INRiM), I-10135 Turin (Italy); D' Aquino, M. [Dipartimento per le Tecnologie, University of Napoli ' Parthenope' , I-80133 Naples (Italy); Bonin, R. [Istituto Nazionale di Ricerca Metrologica (INRiM), I-10135 Turin (Italy)

    2008-02-01

    We consider generalized Landau-Lifshitz-Gilbert (LLG) deterministic dynamics in uniformly magnetized bodies. The dynamics take place on the unit sphere {sigma}, and are characterized by a vector field v tangential to {sigma}. By using Helmholtz decomposition on {sigma}, it is proven that v is uniquely defined by two potentials {chi} and {psi}. Potential {chi} can be identified with the free energy of the system, while {psi} describes non-conservative interactions of the system with the environment. The presence of {psi} modifies the usual energy balance of LLG dynamics. Instead of purely relaxation dynamics we may have steady injection of energy through non-conservative interactions. The implications of the new form of the energy balance are discussed in detail.

  2. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

    Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

  3. Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Kostov, N.A.

    1989-01-01

    In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

  4. Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory

    International Nuclear Information System (INIS)

    Watson, Peter; Alkofer, Reinhard

    2001-01-01

    Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills theory

  5. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...

  6. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    Science.gov (United States)

    Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

    2017-11-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

  7. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    International Nuclear Information System (INIS)

    Hernandez-Walls, R; Martín-Atienza, B; Salinas-Matus, M; Castillo, J

    2017-01-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations. (paper)

  8. Solving Partial Differential Equations Using a New Differential Evolution Algorithm

    Directory of Open Access Journals (Sweden)

    Natee Panagant

    2014-01-01

    Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.

  9. Iteration schemes for parallelizing models of superconductivity

    Energy Technology Data Exchange (ETDEWEB)

    Gray, P.A. [Michigan State Univ., East Lansing, MI (United States)

    1996-12-31

    The time dependent Lawrence-Doniach model, valid for high fields and high values of the Ginzburg-Landau parameter, is often used for studying vortex dynamics in layered high-T{sub c} superconductors. When solving these equations numerically, the added degrees of complexity due to the coupling and nonlinearity of the model often warrant the use of high-performance computers for their solution. However, the interdependence between the layers can be manipulated so as to allow parallelization of the computations at an individual layer level. The reduced parallel tasks may then be solved independently using a heterogeneous cluster of networked workstations connected together with Parallel Virtual Machine (PVM) software. Here, this parallelization of the model is discussed and several computational implementations of varying degrees of parallelism are presented. Computational results are also given which contrast properties of convergence speed, stability, and consistency of these implementations. Included in these results are models involving the motion of vortices due to an applied current and pinning effects due to various material properties.

  10. Perceptual support promotes strategy generation: Evidence from equation solving.

    Science.gov (United States)

    Alibali, Martha W; Crooks, Noelle M; McNeil, Nicole M

    2017-08-30

    Over time, children shift from using less optimal strategies for solving mathematics problems to using better ones. But why do children generate new strategies? We argue that they do so when they begin to encode problems more accurately; therefore, we hypothesized that perceptual support for correct encoding would foster strategy generation. Fourth-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) in a pre-test. They were then randomly assigned to one of three perceptual support conditions or to a Control condition. Participants in all conditions completed three mathematical equivalence problems with feedback about correctness. Participants in the experimental conditions received perceptual support (i.e., highlighting in red ink) for accurately encoding the equal sign, the right side of the equation, or the numbers that could be added to obtain the correct solution. Following this intervention, participants completed a problem-solving post-test. Among participants who solved the problems incorrectly at pre-test, those who received perceptual support for correctly encoding the equal sign were more likely to generate new, correct strategies for solving the problems than were those who received feedback only. Thus, perceptual support for accurate encoding of a key problem feature promoted generation of new, correct strategies. Statement of Contribution What is already known on this subject? With age and experience, children shift to using more effective strategies for solving math problems. Problem encoding also improves with age and experience. What the present study adds? Support for encoding the equal sign led children to generate correct strategies for solving equations. Improvements in problem encoding are one source of new strategies. © 2017 The British Psychological Society.

  11. Development of a set of benchmark problems to verify numerical methods for solving burnup equations

    International Nuclear Information System (INIS)

    Lago, Daniel; Rahnema, Farzad

    2017-01-01

    Highlights: • Description transmutation chain benchmark problems. • Problems for validating numerical methods for solving burnup equations. • Analytical solutions for the burnup equations. • Numerical solutions for the burnup equations. - Abstract: A comprehensive set of transmutation chain benchmark problems for numerically validating methods for solving burnup equations was created. These benchmark problems were designed to challenge both traditional and modern numerical methods used to solve the complex set of ordinary differential equations used for tracking the change in nuclide concentrations over time due to nuclear phenomena. Given the development of most burnup solvers is done for the purpose of coupling with an established transport solution method, these problems provide a useful resource in testing and validating the burnup equation solver before coupling for use in a lattice or core depletion code. All the relevant parameters for each benchmark problem are described. Results are also provided in the form of reference solutions generated by the Mathematica tool, as well as additional numerical results from MATLAB.

  12. A predictor-corrector scheme for solving the Volterra integral equation

    KAUST Repository

    Al Jarro, Ahmed; Bagci, Hakan

    2011-01-01

    The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been

  13. Phase separation and shape deformation of two-phase membranes

    International Nuclear Information System (INIS)

    Jiang, Y.; Lookman, T.; Saxena, A.

    2000-01-01

    Within a coupled-field Ginzburg-Landau model we study analytically phase separation and accompanying shape deformation on a two-phase elastic membrane in simple geometries such as cylinders, spheres, and tori. Using an exact periodic domain wall solution we solve for the shape and phase separating field, and estimate the degree of deformation of the membrane. The results are pertinent to preferential phase separation in regions of differing curvature on a variety of vesicles. (c) 2000 The American Physical Society

  14. Ginzburg criterion for ionic fluids: the effect of Coulomb interactions.

    Science.gov (United States)

    Patsahan, O

    2013-08-01

    The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.

  15. Solving the KPI wave equation with a moving adaptive FEM grid

    Directory of Open Access Journals (Sweden)

    Granville Sewell

    2013-04-01

    Full Text Available The Kadomtsev-Petviashvili I (KPI equation is the difficult nonlinear wave equation $U_{xt} + 6U_x^2 + 6UU_{xx} + U_{xxxx} = 3U_{yy}.$ We solve this equation using PDE2D (www.pde2d.com with initial conditions consisting of two lump solitons, which collide and reseparate. Since the solution has steep, moving, peaks, an adaptive finite element grid is used with a grading which moves with the peaks.

  16. An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    M. Bishehniasar

    2017-01-01

    Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

  17. On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

    International Nuclear Information System (INIS)

    An Hengbin; Mo Zeyao; Xu Xiaowen; Liu Xu

    2009-01-01

    The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.

  18. Time-dependent London approach: Dissipation due to out-of-core normal excitations by moving vortices

    Science.gov (United States)

    Kogan, V. G.

    2018-03-01

    The dissipative currents due to normal excitations are included in the London description. The resulting time-dependent London equations are solved for a moving vortex and a moving vortex lattice. It is shown that the field distribution of a moving vortex loses its cylindrical symmetry. It experiences contraction that is stronger in the direction of the motion than in the direction normal to the velocity v . The London contribution of normal currents to dissipation is small relative to the Bardeen-Stephen core dissipation at small velocities, but it approaches the latter at high velocities, where this contribution is no longer proportional to v2. To minimize the London contribution to dissipation, the vortex lattice is oriented so as to have one of the unit cell vectors along the velocity. This effect is seen in experiments and predicted within the time-dependent Ginzburg-Landau theory.

  19. A method for solving the KDV equation and some numerical experiments

    International Nuclear Information System (INIS)

    Chang Jinjiang.

    1993-01-01

    In this paper, by means of difference method for discretization of space partial derivatives of KDV equation, an initial value problem in ordinary differential equations of large dimensions is produced. By using this ordinary differential equations the existence and the uniqueness of the solution of the KDV equation and the conservation of scheme are proved. This ordinary differential equation can be solved by using implicit Runge-Kutta methods, so a new method for finding the numerical solution of the KDV equation is presented. Numerical experiments not only describe in detail the procedure of two solitons collision, soliton reflex and soliton produce, but also show that this method is very effective. (author). 7 refs, 3 figs

  20. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

    Science.gov (United States)

    Murase, Kenya

    2016-01-01

    Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

  1. Spinor bose gases in cubic optical lattice

    International Nuclear Information System (INIS)

    Mobarak, Mohamed Saidan Sayed Mohamed

    2014-01-01

    In recent years the quantum simulation of condensed-matter physics problems has resulted from exciting experimental progress in the realm of ultracold atoms and molecules in optical lattices. In this thesis we analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons with a linear Zeeman effect, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. To this end we add artificial symmetry-breaking currents to the spin-1 Bose-Hubbard Hamiltonian in order to break the global U (1) symmetry. With this we determine a diagrammatic expansion of the grand-canonical free energy up to fourth order in the symmetry-breaking currents and up to the leading non-trivial order in the hopping strength which is of first order. As a cross-check we demonstrate that the resulting grand-canonical free energy allows to recover the mean-field theory. Applying a Legendre transformation to the grand-canonical free energy, where the symmetry-breaking currents are transformed to order parameters, we obtain the effective Ginzburg-Landau action. With this we calculate in detail at zero temperature the Mott insulator-superfluid quantum phase boundary as well as condensate and particle number density in the superfluid phase. We find that both mean-field and Ginzburg-Landau theory yield the same quantum phase transition between the Mott insulator and superfluid phases, but the range of validity of the mean-field theory turns out to be smaller than that of the Ginzburg-Landau theory. Due to this finding we expect that the Ginzburg-Landau theory gives better results for the superfluid phase and, thus, we restrict ourselves to extremize only the effective Ginzburg-Landau action with respect to the order parameters. Without external magnetic field the superfluid phase is a polar (ferromagnetic) state for anti-ferromagnetic (ferromagnetic) interactions, i.e. only the

  2. An efficient numerical technique for solving navier-stokes equations for rotating flows

    International Nuclear Information System (INIS)

    Haroon, T.; Shah, T.M.

    2000-01-01

    This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)

  3. A control volume based finite difference method for solving the equilibrium equations in terms of displacements

    DEFF Research Database (Denmark)

    Hattel, Jesper; Hansen, Preben

    1995-01-01

    This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....

  4. Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

    Science.gov (United States)

    Issokolo, Remi J. Noumana; Dikandé, Alain M.

    2018-05-01

    A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

  5. Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method

    Directory of Open Access Journals (Sweden)

    Shao-Hong Yan

    2014-01-01

    Full Text Available The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative. The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set.

  6. MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

    KAUST Repository

    Iliev, Oleg; Kirsch, Ralf; Lakdawala, Zahra; Printsypar, Galina

    2014-01-01

    This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid

  7. Intuitive physics knowledge, physics problem solving and the role of mathematical equations

    Directory of Open Access Journals (Sweden)

    Laura Buteler

    2012-09-01

    Full Text Available The present work explores the role that mathematical equations play in modifying students’ physical intuition (diSessa, 1993. The work is carried out assuming that students achieve a great deal of the refinement in their physical intuitions during problem solving (Sherin, 2006. The study is guided by the question of how the use of mathematical equations contributes to this refinement. The authors aim at expanding on Sherin´s (2006 hypothesis, suggesting a more bounding relation between physical intuitions and mathematics. In this scenario, intuitions play a more compelling role in “deciding” which equations are acceptable and which are not. Our hypothesis is constructed on the basis of three cases: the first published by Sherin (2006 and two more from registries of our own. The three cases are compared and analyzed in relation to the role of mathematical equations in refining – or not – the intuitive knowledge students bring to play during problem solving.

  8. Students' errors in solving linear equation word problems: Case ...

    African Journals Online (AJOL)

    kofi.mereku

    Development in most areas of life is based on effective knowledge of science and ... Problem solving, as used in mathematics education literature, refers ... word problems, on the other hand, are those linear equation tasks or ... taught LEWPs in the junior high school, many of them reach the senior high school without a.

  9. Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

    Science.gov (United States)

    Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

    2018-01-01

    This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

  10. Chern-Simons field theory of two-dimensional electrons in the lowest Landau level

    International Nuclear Information System (INIS)

    Zhang, L.

    1996-01-01

    We propose a fermion Chern-Simons field theory describing two-dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest-Landau-level constraint is enforced through a δ functional described by an auxiliary field λ. Unlike the field theory constructed directly with the states in the lowest Landau level, this theory allows one, utilizing the physical picture of open-quote open-quote composite fermion,close-quote close-quote to study the fractional quantum Hall states by mapping them onto certain integer quantum Hall states; but, unlike its application in the unconstrained theory, such a mapping is sensible only when interactions between electrons are present. An open-quote open-quote effective mass,close-quote close-quote which characterizes the scale of low energy excitations in the fractional quantum Hall systems, emerges naturally from our theory. We study a Gaussian effective theory and interpret physically the dressed stationary point equation for λ as an equation for the open-quote open-quote mass renormalization close-quote close-quote of composite fermions. copyright 1996 The American Physical Society

  11. Stability of the nonequilibrium states of a superconductor with a finite difference between the populations of the electron- and hole-like spectral branches

    International Nuclear Information System (INIS)

    Gal'perin, Y.M.; Kozub, V.I.; Spivak, B.Z.

    1981-01-01

    The stability of the nonequilibrium states of a superconductor with a finite difference between the populations of the electron- and hole-like spectral branches is investigated. It is shown that an instability similar to the Cooper instability of a normal metal arises at a sufficiently large value of the imbalance. This eliminates the imbalance within quantum-mechanical (nonkinetic) time periods. The consistency of the allowance for the imbalance in the nonequilibrium Ginzburg-Landau equations is discussed

  12. ELMy-H mode as limit cycle and chaotic oscillations in tokamak plasmas

    International Nuclear Information System (INIS)

    Itoh, Sanae; Itoh, Kimitaka; Fukuyama, Atsushi.

    1991-06-01

    A model of Edge Localized Modes (ELMs) in tokamaks is presented. A limit cycle solution is found in time-dependent Ginzburg Landau type model equation of L/H transition, which has a hysteresis curve between the plasma gradient and flux. The oscillation of edge density appears near the L/H transition boundary. Spatial structure of the intermediate state (mesophase) is obtained in the edge region. Chaotic oscillation is predicted due to random neutrals and external oscillations. (author)

  13. Commensurate vortex configurations in thin superconducting films nanostructured by square lattice of magnetic dots

    Energy Technology Data Exchange (ETDEWEB)

    Milosevic, M.V.; Peeters, F.M

    2004-05-01

    Within the phenomenological Ginzburg-Landau (GL) theory, we investigate the vortex structure of a thin superconducting film (SC) with a regular matrix of ferromagnetic dots (FD) deposited on top of it. The vortex pinning properties of such a magnetic lattice are studied, and the field polarity dependent votex pinning is observed. The exact vortex configuration depends on the size of the magnetic dots, their polarity, periodicity of the FD-rooster and the properties of the SC expressed through the effective Ginzburg-Landau parameter {kappa}*.

  14. Commensurate vortex configurations in thin superconducting films nanostructured by square lattice of magnetic dots

    International Nuclear Information System (INIS)

    Milosevic, M.V.; Peeters, F.M.

    2004-01-01

    Within the phenomenological Ginzburg-Landau (GL) theory, we investigate the vortex structure of a thin superconducting film (SC) with a regular matrix of ferromagnetic dots (FD) deposited on top of it. The vortex pinning properties of such a magnetic lattice are studied, and the field polarity dependent votex pinning is observed. The exact vortex configuration depends on the size of the magnetic dots, their polarity, periodicity of the FD-rooster and the properties of the SC expressed through the effective Ginzburg-Landau parameter κ*

  15. Landau-Zener-Stueckelberg interferometry with low- and high-frequency driving

    Science.gov (United States)

    Shevchenko, Sergey; Ashhab, Sahel; Nori, Franco

    2010-03-01

    The problem of a periodically driven two-level system cannot be solved exactly. The rotating-wave approximation (RWA) is the most common approximation used to analyze this problem. I will discuss an alternative approximation that applies in the case of very strong driving, where the RWA is generally invalid. The dynamics is approximated by a sequence of Landau-Zener transitions that can interfere constructively or destructively, depending on the Stueckelberg phase accumulated between transitions. It turns out that the resonance conditions are qualitatively different for the cases of low- and high-frequency driving. I will discuss the two respective limits. I will also show that our theoretical results describe recent experiments on Landau-Zener-Stuckelberg interferometry with superconducting qubits [S.N. Shevchenko, S. Ashhab, and F. Nori, arXiv:0911.1917].

  16. Various Newton-type iterative methods for solving nonlinear equations

    Directory of Open Access Journals (Sweden)

    Manoj Kumar

    2013-10-01

    Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.

  17. An efficient numerical method for solving the Boltzmann equation in multidimensions

    Science.gov (United States)

    Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas

    2018-01-01

    In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.

  18. A Python Program for Solving Schro¨dinger's Equation in Undergraduate Physical Chemistry

    Science.gov (United States)

    Srnec, Matthew N.; Upadhyay, Shiv; Madura, Jeffry D.

    2017-01-01

    In undergraduate physical chemistry, Schrödinger's equation is solved for a variety of cases. In doing so, the energies and wave functions of the system can be interpreted to provide connections with the physical system being studied. Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming…

  19. MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

    KAUST Repository

    Iliev, Oleg

    2014-01-01

    This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid with a sophisticated finite volume method, namely MPFA O-method, is used to discretize the system of equations. Numerical results for two examples are presented, namely, channel flow and flow in a ring with a rolled porous medium. © Springer International Publishing Switzerland 2014.

  20. A matrix formalism to solve interface condition equations in a reactor system

    Energy Technology Data Exchange (ETDEWEB)

    Matausek, M V [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)

    1970-05-15

    When a nuclear reactor or a reactor lattice cell is treated by an approximate procedure to solve the neutron transport equation, as the last computational step often appears a problem of solving systems of algebraic equations stating the interface and boundary conditions for the neutron flux moments. These systems have usually the coefficient matrices of the block-bi diagonal type, containing thus a large number of zero elements. In the present report it is shown how such a system can be solved efficiently accounting for all the zero elements both in the coefficient matrix and in the free term vector. The procedure is presented here for the case of multigroup P{sub 3} calculation of neutron flux distribution in a cylindrical reactor lattice cell. Compared with the standard gaussian elimination method, this procedure is more advantageous both in respect to the number of operations needed to solve a given problem and in respect to the computer memory storage requirements. A similar formalism can also be applied for other approximate methods, for instance for multigroup diffusion treatment of a multi zone reactor. (author)

  1. Space-time spectral collocation algorithm for solving time-fractional Tricomi-type equations

    Directory of Open Access Journals (Sweden)

    Abdelkawy M.A.

    2016-01-01

    Full Text Available We introduce a new numerical algorithm for solving one-dimensional time-fractional Tricomi-type equations (T-FTTEs. We used the shifted Jacobi polynomials as basis functions and the derivatives of fractional is evaluated by the Caputo definition. The shifted Jacobi Gauss-Lobatt algorithm is used for the spatial discretization, while the shifted Jacobi Gauss-Radau algorithmis applied for temporal approximation. Substituting these approximations in the problem leads to a system of algebraic equations that greatly simplifies the problem. The proposed algorithm is successfully extended to solve the two-dimensional T-FTTEs. Extensive numerical tests illustrate the capability and high accuracy of the proposed methodologies.

  2. Inter plane coupling and magnetic properties in a high Tc superconductor

    International Nuclear Information System (INIS)

    Malacarne, L.C.; Mendes, R.S.; Veroneze, P.R.

    1997-01-01

    We investigate if besides an increasing in T c , an interaction favoring pair tunneling reproduces some characteristic properties of the superconductors, in the presence of a magnetic field. With this objective, we use a sufficiently simple Hamiltonian which maintains the main qualitative aspects of the inter plane interaction through pairs. We also apply an functional integration method for obtaining the Landau-Ginzburg (L G) equations in presence of magnetic field. From these equations, we verify that the applied model presents the properties expected for a superconductor, e.g. magnetic flux quantization, Meissner effect and possible existence of vortex and vortex lattice

  3. A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mountassir Hamdi Cherif

    2017-11-01

    Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

  4. Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

    International Nuclear Information System (INIS)

    Tao Ganqiang; Yu Qing; Xiao Xiao

    2011-01-01

    Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

  5. Application of Trotter approximation for solving time dependent neutron transport equation

    International Nuclear Information System (INIS)

    Stancic, V.

    1987-01-01

    A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)

  6. Variations on the planar Landau problem: canonical transformations, a purely linear potential and the half-plane

    International Nuclear Information System (INIS)

    Govaerts, Jan; Hounkonnou, M Norbert; Mweene, Habatwa V

    2009-01-01

    The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well.

  7. Variations on the planar Landau problem: canonical transformations, a purely linear potential and the half-plane

    Energy Technology Data Exchange (ETDEWEB)

    Govaerts, Jan [Center for Particle Physics and Phenomenology (CP3), Institut de Physique Nucleaire, Universite catholique de Louvain (UCL), 2, Chemin du Cyclotron, B-1348 Louvain-la Neuve (Belgium); Hounkonnou, M Norbert [International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, 072 BP 50, Cotonou (Benin); Mweene, Habatwa V [Physics Department, University of Zambia, PO Box 32379, Lusaka (Zambia)], E-mail: Jan.Govaerts@uclouvain.be, E-mail: hounkonnou@yahoo.fr, E-mail: norbert.hounkonnou@cipma.uac.bj, E-mail: habatwamweene@yahoo.com, E-mail: hmweene@unza.zm

    2009-12-04

    The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well.

  8. An Unconditionally Stable Method for Solving the Acoustic Wave Equation

    Directory of Open Access Journals (Sweden)

    Zhi-Kai Fu

    2015-01-01

    Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.

  9. Factors Affecting Differential Equation Problem Solving Ability of Students at Pre-University Level: A Conceptual Model

    Science.gov (United States)

    Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen

    2017-01-01

    In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…

  10. Explosions in Landau Vlasov dynamics

    International Nuclear Information System (INIS)

    Suraud, E.; Cussol, D.; Gregoire, C.; Boilley, D.; Pi, M.; Schuck, P.; Remaud, B.; Sebille, F.

    1988-01-01

    A microscopic study of the quasi-fusion/explosion transition is presented in the framework of Landau-Vlasov simulations of intermediate energy heavy-ion collisions (bombarding energies between 10 and 100 MeV/A). A detailed analysis in terms of the Equation of State of the system is performed. In agreement with schematic models we find that the composite nuclear system formed in the collision does explode when it stays long enough in the mechanically unstable region (spinodal region). Quantitative estimates of the explosion threshold are given for central symmetric reactions (Ca+Ca and Ar+Ti). The effect of the nuclear matter compressibility modulus is discussed

  11. An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

    Science.gov (United States)

    Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

    2017-11-01

    Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

  12. Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

    Science.gov (United States)

    Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

    2015-01-01

    The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

  13. A homotopy method for solving Riccati equations on a shared memory parallel computer

    International Nuclear Information System (INIS)

    Zigic, D.; Watson, L.T.; Collins, E.G. Jr.; Davis, L.D.

    1993-01-01

    Although there are numerous algorithms for solving Riccati equations, there still remains a need for algorithms which can operate efficiently on large problems and on parallel machines. This paper gives a new homotopy-based algorithm for solving Riccati equations on a shared memory parallel computer. The central part of the algorithm is the computation of the kernel of the Jacobian matrix, which is essential for the corrector iterations along the homotopy zero curve. Using a Schur decomposition the tensor product structure of various matrices can be efficiently exploited. The algorithm allows for efficient parallelization on shared memory machines

  14. Adomian decomposition method for solving the telegraph equation in charged particle transport

    International Nuclear Information System (INIS)

    Abdou, M.A.

    2005-01-01

    In this paper, the analysis for the telegraph equation in case of isotropic small angle scattering from the Boltzmann transport equation for charged particle is presented. The Adomian decomposition is used to solve the telegraph equation. By means of MAPLE the Adomian polynomials of obtained series (ADM) solution have been calculated. The behaviour of the distribution function are shown graphically. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solution of linear and nonlinear problems

  15. Towards a generalized Landau theory of quasi-particles for hot dense matter

    International Nuclear Information System (INIS)

    Leermakers, R.

    1985-01-01

    In this thesis it is tried to construct a Landau quasi-particle theory for relativistic systems, using field-theoretical methods. It includes a perturbative calculation of the pressure of a quark-gluon plasma. It reports the existence of a hitherto unnoticed plasmon contribution of the order g 3 due to transverse quasi-gluons. A new and Lorentz covariant formulation of the Landau theory is being developed, for a general relativistic system. A detailed calculation is presented of the observables of a quantum electrodynamical (QED) plasma, in lowest orders of perturbation theory. A transverse plasmon effect is discovered, both analytically and numerically. In addition, the analysis shows quasi-electrons and positrons to be stable excitations at any temperature. This is proven in all orders of perturbation theory. Along with a Landau theory for quark-gluon matter, a linearized kinetic equation is derived for the singlet quark distribution function, with a collision term for soft encounters between quasi-quarks. (Auth.)

  16. Rogue waves in a water tank: Experiments and modeling

    Science.gov (United States)

    Lechuga, Antonio

    2013-04-01

    Recently many rogue waves have been reported as the main cause of ship incidents on the sea. One of the main characteristics of rogue waves is its elusiveness: they present unexpectedly and disappear in the same wave. Some authors (Zakharov and al.2010) are attempting to find the probability of their appearances apart from studyingthe mechanism of the formation. As an effort on this topic we tried the generation of rogue waves in a water wave tank using a symmetric spectrum(Akhmediev et al. 2011) as input on the wave maker. The produced waves were clearly rogue waves with a rate (maximum wave height/ Significant wave height) of 2.33 and a kurtosis of 4.77 (Janssen 2003, Onorato 2006). These results were already presented (Lechuga 2012). Similar waves (in pattern aspect, but without being extreme waves) were described as crossing waves in a water tank(Shemer and Lichter1988). To go on further the next step has been to apply a theoretical model to the envelope of these waves. After some considerations the best model has been an analogue of the Ginzburg-Landau equation. This apparently amazing result is easily explained: We know that the Ginzburg-Landau model is related to some regular structures on the surface of a liquid and also in plasmas, electric and magnetic fields and other media. Another important characteristic of the model is that their solutions are invariants with respectto the translation group. The main aim of this presentation is to extract conclusions of the model and the comparison with the measured waves in the water tank.The nonlinear structure of waves and their regularity make suitable the use of the Ginzburg-Landau model to the envelope of generated waves in the tank,so giving us a powerful tool to cope with the results of our experiment.

  17. Dependence of the ferroelectric domain shape on the electric field of the microscope tip

    International Nuclear Information System (INIS)

    Starkov, Alexander S.; Starkov, Ivan A.

    2015-01-01

    A theory of an equilibrium shape of the domain formed in an electric field of a scanning force microscope (SFM) tip is proposed. We do not assume a priori that the domain has a fixed form. The shape of the domain is defined by the minimum of the free energy of the ferroelectric. This energy includes the energy of the depolarization field, the energy of the domain wall, and the energy of the interaction between the domain and the electric field of the SFM tip. The contributions of the apex and conical part of the tip are examined. Moreover, in the proposed approach, any narrow tip can be considered. The surface energy is determined on the basis of the Ginzburg-Landau-Devonshire theory and takes into account the curvature of the domain wall. The variation of the free energy with respect to the domain shape leads to an integro-differential equation, which must be solved numerically. Model results are illustrated for lithium tantalate ceramics

  18. The discontinuous finite element method for solving Eigenvalue problems of transport equations

    International Nuclear Information System (INIS)

    Yang, Shulin; Wang, Ruihong

    2011-01-01

    In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)

  19. The H-N method for solving linear transport equation: theory and application

    International Nuclear Information System (INIS)

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  20. A novel method to solve functional differential equations

    International Nuclear Information System (INIS)

    Tapia, V.

    1990-01-01

    A method to solve differential equations containing the variational operator as the derivation operation is presented. They are called variational differential equations (VDE). The solution to a VDE should be a function containing the derivatives, with respect to the base space coordinates, of the fields up to a generic order s: a s-th-order function. The variational operator doubles the order of the function on which it acts. Therefore, in order to make compatible the orders of the different terms appearing in a VDE, the solution should be a function containing the derivatives of the fields at all orders. But this takes us again back to the functional methods. In order to avoid this, one must restrict the considerations, in the case of second-order VDEs, to the space of s-th-order functions on which the variational operator acts transitively. These functions have been characterized for a one-dimensional base space for the first- and second-order cases. These functions turn out to be polynomial in the highest-order derivatives of the fields with functions of the lower-order derivatives as coefficients. Then VDEs reduce to a system of coupled partial differential equations for the coefficients above mentioned. The importance of the method lies on the fact that the solutions to VDEs are in a one-to-one correspondence with the solutions of functional differential equations. The previous method finds direct applications in quantum field theory, where the Schroedinger equation plays a central role. Since the Schroedinger equation is reduced to a system of coupled partial differential equations, this provides a nonperturbative scheme for quantum field theory. As an example, the massless scalar field is considered

  1. Solving Linear Equations by Classical Jacobi-SR Based Hybrid Evolutionary Algorithm with Uniform Adaptation Technique

    OpenAIRE

    Jamali, R. M. Jalal Uddin; Hashem, M. M. A.; Hasan, M. Mahfuz; Rahman, Md. Bazlar

    2013-01-01

    Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods especially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxation factor, {\\omega}. Recently, hybridization of classical Gauss-Seidel based successive relaxation t...

  2. Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

    Directory of Open Access Journals (Sweden)

    Mohammad Almousa

    2013-01-01

    Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.

  3. Damped nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Nicholson, D.R.; Goldman, M.V.

    1976-01-01

    High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time

  4. A toolbox to solve coupled systems of differential and difference equations

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de

    2016-01-01

    We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.

  5. A toolbox to solve coupled systems of differential and difference equations

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Linz Univ. (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [DESY Zeuthen (Germany)

    2016-01-15

    We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.

  6. The ATOMFT integrator - Using Taylor series to solve ordinary differential equations

    Science.gov (United States)

    Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.

    1988-01-01

    This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.

  7. Numerical methods for solving the governing equations for a seriated continuum

    International Nuclear Information System (INIS)

    Narum, R.E.; Noble, C.; Mortensen, G.A.; McFadden, J.H.

    1976-09-01

    A desire to more accurately predict the behavior of transient two-phase flows has resulted in an investigation of the feasibility of computing unequal phase velocities and unequal phase temperatures. The finite difference forms of a set of equations governing a seriated continuum are presented along with two methods developed for solving the resulting systems of simultaneous nonlinear equations. Results from a one-dimensional computer code are presented to illustrate the capabilities of one of the solution methods

  8. Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

    International Nuclear Information System (INIS)

    Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.

    2011-01-01

    The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)

  9. Relativistic electron beam acceleration by cascading nonlinear Landau damping of electromagnetic waves in a plasma

    International Nuclear Information System (INIS)

    Sugaya, R.; Ue, A.; Maehara, T.; Sugawa, M.

    1996-01-01

    Acceleration and heating of a relativistic electron beam by cascading nonlinear Landau damping involving three or four intense electromagnetic waves in a plasma are studied theoretically based on kinetic wave equations and transport equations derived from relativistic Vlasov endash Maxwell equations. Three or four electromagnetic waves excite successively two or three nonresonant beat-wave-driven relativistic electron plasma waves with a phase velocity near the speed of light [v p =c(1-γ -2 p ) 1/2 , γ p =ω/ω pe ]. Three beat waves interact nonlinearly with the electron beam and accelerate it to a highly relativistic energy γ p m e c 2 more effectively than by the usual nonlinear Landau damping of two electromagnetic waves. It is proved that the electron beam can be accelerated to more highly relativistic energy in the plasma whose electron density decreases temporally with an appropriate rate because of the temporal increase of γ p . copyright 1996 American Institute of Physics

  10. A Simple Derivation of Kepler's Laws without Solving Differential Equations

    Science.gov (United States)

    Provost, J.-P.; Bracco, C.

    2009-01-01

    Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

  11. Using packaged software for solving two differential equation problems that arise in plasma physics

    International Nuclear Information System (INIS)

    Gaffney, P.W.

    1980-01-01

    Experience in using packaged numerical software for solving two related problems that arise in Plasma physics is described. These problems are (i) the solution of the reduced resistive MHD equations and (ii) the solution of the Grad-Shafranov equation

  12. Time-Dependent Heat Conduction Problems Solved by an Integral-Equation Approach

    International Nuclear Information System (INIS)

    Oberaigner, E.R.; Leindl, M.; Antretter, T.

    2010-01-01

    Full text: A classical task of mathematical physics is the formulation and solution of a time dependent thermoelastic problem. In this work we develop an algorithm for solving the time-dependent heat conduction equation c p ρ∂ t T-kT, ii =0 in an analytical, exact fashion for a two-component domain. By the Green's function approach the formal solution of the problem is obtained. As an intermediate result an integral-equation for the temperature history at the domain interface is formulated which can be solved analytically. This method is applied to a classical engineering problem, i.e. to a special case of a Stefan-Problem. The Green's function approach in conjunction with the integral-equation method is very useful in cases were strong discontinuities or jumps occur. The initial conditions and the system parameters of the investigated problem give rise to two jumps in the temperature field. Purely numerical solutions are obtained by using the FEM (finite element method) and the FDM (finite difference method) and compared with the analytical approach. At the domain boundary the analytical solution and the FEM-solution are in good agreement, but the FDM results show a signicant smearing effect. (author)

  13. Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation

    Energy Technology Data Exchange (ETDEWEB)

    Xia, Yin [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); University of Chinese Academy of Science, Beijing 100049 (China); Xu, Jun, E-mail: xujun@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); Li, Bao-An [Department of Physics and Astronomy, Texas A& M University-Commerce, Commerce, TX 75429-3011 (United States); Department of Applied Physics, Xi' an Jiao Tong University, Xi' an 710049 (China); Shen, Wen-Qing [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China)

    2016-08-10

    A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann–Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin–orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.

  14. New numerical method for solving the solute transport equation

    International Nuclear Information System (INIS)

    Ross, B.; Koplik, C.M.

    1978-01-01

    The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

  15. Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

    International Nuclear Information System (INIS)

    Pletzer, A.; Zakharov, L.E.

    1999-01-01

    The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory

  16. Insights into the School Mathematics Tradition from Solving Linear Equations

    Science.gov (United States)

    Buchbinder, Orly; Chazan, Daniel; Fleming, Elizabeth

    2015-01-01

    In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

  17. Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

    Science.gov (United States)

    Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

    2013-06-01

    In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

  18. On Landau Scenario of Chaotization for Beam Distribution

    International Nuclear Information System (INIS)

    Parsa, Z.; Zadorozhny, V.

    1999-01-01

    We examine a problem in nonlinear dynamics in which both regular and chaotic motions are possible. Thus we deal with some of the fundamental theoretical problem of accelerator physics, mathematics theory of dynamical systems, and other fields of physics. The focus is on the appearance of chaos in a beam distribution. A study of the problem is based on two observations. The First observation is that using Lyapunov method and its extension we obtain solutions of partial differential equations. Using this approach we discuss the problem of finding a solution of Vlasov-Poisson equation, i.e., some stationary solution where we consider magnetic field as some disturbance with a small parameter. Thus the solution of Vlasov equation yields an asymptotic series such that the solution of Vlasov-Poisson equation is the basis solution for one. The second observation is that physical chaos is weakly limit of, well known, the Landau bifurcation's. This fact we have proved using ideas on the Nature of Turbulence

  19. A pertinent approach to solve nonlinear fuzzy integro-differential equations.

    Science.gov (United States)

    Narayanamoorthy, S; Sathiyapriya, S P

    2016-01-01

    Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

  20. A Fortran program (RELAX3D) to solve the 3 dimensional Poisson (Laplace) equation

    International Nuclear Information System (INIS)

    Houtman, H.; Kost, C.J.

    1983-09-01

    RELAX3D is an efficient, user friendly, interactive FORTRAN program which solves the Poisson (Laplace) equation Λ 2 =p for a general 3 dimensional geometry consisting of Dirichlet and Neumann boundaries approximated to lie on a regular 3 dimensional mesh. The finite difference equations at these nodes are solved using a successive point-iterative over-relaxation method. A menu of commands, supplemented by HELP facility, controls the dynamic loading of the subroutine describing the problem case, the iterations to converge to a solution, and the contour plotting of any desired slices, etc

  1. Solving Differential Equations Analytically. Elementary Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 335.

    Science.gov (United States)

    Goldston, J. W.

    This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

  2. Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential

    International Nuclear Information System (INIS)

    Zhang Ying; Liang Haozhao; Meng Jie

    2009-01-01

    The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus 12 C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.

  3. A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves

    Science.gov (United States)

    Favrie, N.; Gavrilyuk, S.

    2017-07-01

    A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.

  4. Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

    Science.gov (United States)

    Kougias, Ioannis E.

    2009-01-01

    Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

  5. On the Efficiency of Algorithms for Solving Hartree–Fock and Kohn–Sham Response Equations

    DEFF Research Database (Denmark)

    Kauczor, Joanna; Jørgensen, Poul; Norman, Patrick

    2011-01-01

    The response equations as occurring in the Hartree–Fock, multiconfigurational self-consistent field, and Kohn–Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors...

  6. Theory of fractional quantum Hall effect

    International Nuclear Information System (INIS)

    Kostadinov, I.Z.

    1984-09-01

    A theory of the fractional quantum Hall effect is constructed by introducing 3-particle interactions breaking the symmetry for ν=1/3 according to a degeneracy theorem proved here. An order parameter is introduced and a gap in the single particle spectrum is found. The critical temperature, critical filling number and critical behaviour are determined as well as the Ginzburg-Landau equation coefficients. A first principle calculation of the Hall current is given. 3, 5, 7 electron tunneling and Josephson interference effects are predicted. (author)

  7. Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

    Science.gov (United States)

    Kozitskiy, Sergey

    2018-05-01

    Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

  8. The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Behzad Ghanbari

    2014-01-01

    Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

  9. New Efficient Fourth Order Method for Solving Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Farooq Ahmad

    2013-12-01

    Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

  10. A parallel algorithm for solving the integral form of the discrete ordinates equations

    International Nuclear Information System (INIS)

    Zerr, R. J.; Azmy, Y. Y.

    2009-01-01

    The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)

  11. New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

    Science.gov (United States)

    Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

    2014-01-01

    In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

  12. A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

    KAUST Repository

    Wu, Zedong

    2018-04-05

    Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

  13. Solving Kepler's equation using implicit functions

    Science.gov (United States)

    Mortari, Daniele; Elipe, Antonio

    2014-01-01

    A new approach to solve Kepler's equation based on the use of implicit functions is proposed here. First, new upper and lower bounds are derived for two ranges of mean anomaly. These upper and lower bounds initialize a two-step procedure involving the solution of two implicit functions. These two implicit functions, which are non-rational (polynomial) Bézier functions, can be linear or quadratic, depending on the derivatives of the initial bound values. These are new initial bounds that have been compared and proven more accurate than Serafin's bounds. The procedure reaches machine error accuracy with no more that one quadratic and one linear iterations, experienced in the "tough range", where the eccentricity is close to one and the mean anomaly to zero. The proposed method is particularly suitable for space-based applications with limited computational capability.

  14. Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2013-01-01

    Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

  15. Modeling Blazar Spectra by Solving an Electron Transport Equation

    Science.gov (United States)

    Lewis, Tiffany; Finke, Justin; Becker, Peter A.

    2018-01-01

    Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.

  16. Scattering of a two skyrmion configuration on potential holes or barriers in a model Landau-Lifshitz equation

    International Nuclear Information System (INIS)

    Collins, J C; Zakrzewski, W J

    2009-01-01

    The dynamics of a baby-skyrmion configuration, in a model Landau-Lifshitz equation, was studied in the presence of various potential obstructions. The baby-skyrmion configuration was constructed from two Q = 1 hedgehog solutions to the baby-skyrme model in (2+1) dimensions. The potential obstructions were created by introducing a new term into the Lagrangian which resulted in a localized inhomogeneity in the potential terms' coefficient. In the barrier system, the normal circular path was deformed as the skyrmions traversed the barrier. During the same period, it was seen that the skyrmions sped up as they went over the barrier. For critical values of the barrier height and width, the skyrmions were no longer bound and were free to separate. In the case of a potential hole, the baby skyrmions no longer formed a bound state and moved asymptotically along the axis of the hole. It is shown how to modify the definition of the angular momentum to include the effects of the obstructions, so that it is conserved

  17. Solving the transport equation with quadratic finite elements: Theory and applications

    International Nuclear Information System (INIS)

    Ferguson, J.M.

    1997-01-01

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids

  18. Recent advances in marching-on-in-time schemes for solving time domain volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan

    2015-01-01

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.

  19. Recent advances in marching-on-in-time schemes for solving time domain volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin

    2015-05-16

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.

  20. Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

    Energy Technology Data Exchange (ETDEWEB)

    Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)

    2007-01-15

    In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.

  1. Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

    Science.gov (United States)

    Didis, Makbule Gozde; Erbas, Ayhan Kursat

    2015-01-01

    This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…

  2. Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

    Science.gov (United States)

    Macias-Medri, A. E.; Rodríguez-Núñez, J. J.

    2018-05-01

    A two-band and quartic interaction order Ginzburg-Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter γ) and fourth (quartic, with coupling parameter γ˜) order between the two superconducting order parameters (fi with i = 1,2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the fi-profiles, where our starting point was the calculation of the superconducting critical temperature Tc. With this at hand, we evaluate fi and the magnetic field along the z-axis, B0, as function of γ, γ˜, the radial distance r/λ1(0) and the temperature T, for T ≈ Tc. The self-consistent equations allow us to compute λ (penetration depth) and the healing lengths of fi (Lhi with i = 1,2) as functions of T, γ and γ˜. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.

  3. Boundary conditions in Ginsburg Landau theory and critical temperature of high-T superconductors

    Science.gov (United States)

    Lykov, A. N.

    2008-06-01

    New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature ( T) of high- T superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T of cuprate superconductors.

  4. Solving Some Special Cases of Monomial Ratio Equations Appearing Frequently in Physical and Engineering Problems

    Directory of Open Access Journals (Sweden)

    Enrique Castillo

    2016-01-01

    Full Text Available We first show that monomial ratio equations are not only very common in Physics and Engineering, but the natural type of equations in many practical problems. More precisely, in the case of models involving scale variables if the used formulas are not of this type they are not physically valid. The consequence is that when estimating the model parameters we are faced with systems of monomial ratio equations that are nonlinear and difficult to solve. In this paper, we provide an original algorithm to obtain the unique solutions of systems of equations made of linear combinations of monomial ratios whose coefficient matrix has a proper null space with low dimension that permits solving the problem in a simple way. Finally, we illustrate the proposed methods by their application to two practical problems from the hydraulic and structural fields.

  5. A Method for Solving the Voltage and Torque Equations of the Split-Phase Induction Machines

    Directory of Open Access Journals (Sweden)

    G. A. Olarinoye

    2013-06-01

    Full Text Available Single phase induction machines have been the subject of many researches in recent times. The voltage and torque equations which describe the dynamic characteristics of these machines have been quoted in many papers, including the papers that present the simulation results of these model equations. The way and manner in which these equations are solved is not common in literature. This paper presents a detailed procedure of how these equations are to be solved with respect to the splitphase induction machine which is one of the different types of the single phase induction machines available in the market. In addition, these equations have been used to simulate the start-up response of the split phase induction motor on no-load. The free acceleration characteristics of the motor voltages, currents and electromagnetic torque have been plotted and discussed. The simulation results presented include the instantaneous torque-speed characteristics of the Split phase Induction machine. A block diagram of the method for the solution of the machine equations has also been presented.

  6. Transit-Time Damping, Landau Damping, and Perturbed Orbits

    Science.gov (United States)

    Simon, A.; Short, R. W.

    1997-11-01

    Transit-time damping(G.J. Morales and Y.C. Lee, Phys. Rev. Lett. 33), 1534 (1974).*^,*(P.A. Robinson, Phys. Fluids B 3), 545 (1991).** has traditionally been obtained by calculating the net energy gain of transiting electrons, of velocity v, to order E^2* in the amplitude of a localized electric field. This necessarily requires inclusion of the perturbed orbits in the equation of motion. A similar method has been used by others(D.R. Nicholson, Introduction to Plasma Theory) (Wiley, 1983).*^,*(E.M. Lifshitz and L.P. Pitaevskifi, Physical Kinetics) (Pergamon, 1981).** to obtain a ``physical'' picture of Landau damping in a nonlocalized field. The use of perturbed orbits seems odd since the original derivation of Landau (and that of Dawson) never went beyond a linear picture of the dynamics. We introduce a novel method that takes advantage of the time-reversal invariance of the Vlasov equation and requires only the unperturbed orbits to obtain the result. Obviously, there is much reduction in complexity. Application to finite slab geometry yields a simple expression for the damping rate. Equivalence to much more complicated results^2* is demonstrated. This method allows us to calculate damping in more complicated geometries and more complex electric fields, such as occur in SRS in filaments. See accompanying talk.(R.W. Short and A. Simon, this conference.) This work was supported by the U.S. DOE Office of Inertial Confinement Fusion under Co-op Agreement No. DE-FC03-92SF19460.

  7. A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations.

    Science.gov (United States)

    Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere

    2015-04-01

    This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.

  8. The spectral transform as a tool for solving nonlinear discrete evolution equations

    International Nuclear Information System (INIS)

    Levi, D.

    1979-01-01

    In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

  9. Hermite Functional Link Neural Network for Solving the Van der Pol-Duffing Oscillator Equation.

    Science.gov (United States)

    Mall, Susmita; Chakraverty, S

    2016-08-01

    Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.

  10. Landau Damping Revisited

    International Nuclear Information System (INIS)

    Rees, John; Chao, Alexander

    2008-01-01

    Landau damping, as the term is used in accelerator science, is a physical process in which an ensemble of harmonic oscillators--an accelerator beam, for example--that would otherwise be unstable is stabilized by a spread in the natural frequencies of the oscillators. This is a study of the most basic aspects of that process. It has two main goals: to gain a deeper insight into the mechanism of Landau damping and to find the coherent motion of the ensemble and thus the dependence of the total damping rate on the frequency spread

  11. Guiding brine shrimp through mazes by solving reaction diffusion equations

    Science.gov (United States)

    Singal, Krishma; Fenton, Flavio

    Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.

  12. Deterministic methods to solve the integral transport equation in neutronic

    International Nuclear Information System (INIS)

    Warin, X.

    1993-11-01

    We present a synthesis of the methods used to solve the integral transport equation in neutronic. This formulation is above all used to compute solutions in 2D in heterogeneous assemblies. Three kinds of methods are described: - the collision probability method; - the interface current method; - the current coupling collision probability method. These methods don't seem to be the most effective in 3D. (author). 9 figs

  13. On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

    Directory of Open Access Journals (Sweden)

    Hameed Husam Hameed

    2015-01-01

    Full Text Available We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

  14. A mixed Fourier–Galerkin–finite-volume method to solve the fluid dynamics equations in cylindrical geometries

    International Nuclear Information System (INIS)

    Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M

    2012-01-01

    We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)

  15. Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

    Science.gov (United States)

    Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

    2016-06-01

    The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

  16. Singularity spectrum of self-organized criticality

    International Nuclear Information System (INIS)

    Canessa, E.

    1992-10-01

    I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality. Numerical support is given by a comparison with reported simulation data. Within the theory the origin of self-organized critical phenomena is analysed in terms of a nonlinear singularity spectrum different form the typical convex shape due to multifractal measures. (author). 29 refs, 5 figs

  17. Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems

    International Nuclear Information System (INIS)

    Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.

    1994-01-01

    This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)

  18. London limit for lattice model of superconductor

    International Nuclear Information System (INIS)

    Ktitorov, S.A.

    2004-01-01

    The phenomenological approach to the strong-bond superconductor, which is based on the Ginzburg-Landau equation in the London limit, is considered. The effect of the crystalline lattice discreteness on the superconductors electromagnetic properties is studied. The classic problems on the critical current and magnetic field penetration are studied within the frames of the lattice model for thin superconducting films. The dependence of the superconducting current on the thin film order parameter is obtained. The critical current dependence on the degree of deviation from the continual approximation is calculated [ru

  19. Ostwald ripening theory. Final Report, 3 October 1984-1 June 1986

    International Nuclear Information System (INIS)

    Baird, J.K.

    1986-06-01

    The Ostwald-ripening theory is deduced and discussed starting from the fundamental principles such as Ising model concept, Mayer cluster expansion, Langer condensation point theory, Ginzburg-Landau free energy, Stillinger cutoff-pair potential, LSW-theory and MLSW-theory. Mathematical intricacies are reduced to an understanding version. Comparison of selected works, from 1949 to 1984, on solution of diffusion equation with and without sink/sources term(s) is presented. Kahlweit's 1980 work and Marqusee-Ross' 1954 work are more emphasized. Odijk and Lekkerkerker's 1985 work on rodlike macromolecules is introduced in order to simulate interested investigators

  20. Domain decomposition method for solving the neutron diffusion equation

    International Nuclear Information System (INIS)

    Coulomb, F.

    1989-03-01

    The aim of this work is to study methods for solving the neutron diffusion equation; we are interested in methods based on a classical finite element discretization and well suited for use on parallel computers. Domain decomposition methods seem to answer this preoccupation. This study deals with a decomposition of the domain. A theoretical study is carried out for Lagrange finite elements and some examples are given; in the case of mixed dual finite elements, the study is based on examples [fr

  1. From Euclidean to Minkowski space with the Cauchy-Riemann equations

    International Nuclear Information System (INIS)

    Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.

    2008-01-01

    We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)

  2. A simple derivation of Kepler's laws without solving differential equations

    International Nuclear Information System (INIS)

    Provost, J-P; Bracco, C

    2009-01-01

    Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to an explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by undergraduates or by secondary school teachers (who might use it with their pupils), can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

  3. Landau fluid models of collisionless magnetohydrodynamics

    International Nuclear Information System (INIS)

    Snyder, P.B.; Hammett, G.W.; Dorland, W.

    1997-01-01

    A closed set of fluid moment equations including models of kinetic Landau damping is developed which describes the evolution of collisionless plasmas in the magnetohydrodynamic parameter regime. The model is fully electromagnetic and describes the dynamics of both compressional and shear Alfven waves, as well as ion acoustic waves. The model allows for separate parallel and perpendicular pressures p parallel and p perpendicular , and, unlike previous models such as Chew-Goldberger-Low theory, correctly predicts the instability threshold for the mirror instability. Both a simple 3 + 1 moment model and a more accurate 4 + 2 moment model are developed, and both could be useful for numerical simulations of astrophysical and fusion plasmas

  4. Synergetcs - a field beyond irreversible thermodynamics

    International Nuclear Information System (INIS)

    Haken, H.

    1978-01-01

    This lecture introduces the reader to synergetics, a very young field of interdisciplinary research, which is devoted to the question of self-organization and, quite generally, to the birth of new qualities. After comparing the role of thermodynamics, irreversible thermodynamics and synergetics in the description of phenomena we give a few examples for self-oragnizing systems. Next we outline the mathematical approach and consider the generalized Ginzburg-Landau equations for non equilibrium phase transitions. We continue by applying these equations to the problem of morphogenesis in biology. We close our lecture by extending the formalism to spatially inhomogeneous or oscillating systems and arrive at order-parameter equations which are capable of describing new large classes of higher bifurcation schemes. (HJ)

  5. Comparative Assessment of Nonlocal Continuum Solvent Models Exhibiting Overscreening

    Directory of Open Access Journals (Sweden)

    Ren Baihua

    2017-01-01

    Full Text Available Nonlocal continua have been proposed to offer a more realistic model for the electrostatic response of solutions such as the electrolyte solvents prominent in biology and electrochemistry. In this work, we review three nonlocal models based on the Landau-Ginzburg framework which have been proposed but not directly compared previously, due to different expressions of the nonlocal constitutive relationship. To understand the relationships between these models and the underlying physical insights from which they are derive, we situate these models into a single, unified Landau-Ginzburg framework. One of the models offers the capacity to interpret how temperature changes affect dielectric response, and we note that the variations with temperature are qualitatively reasonable even though predictions at ambient temperatures are not quantitatively in agreement with experiment. Two of these models correctly reproduce overscreening (oscillations between positive and negative polarization charge densities, and we observe small differences between them when we simulate the potential between parallel plates held at constant potential. These computations require reformulating the two models as coupled systems of local partial differential equations (PDEs, and we use spectral methods to discretize both problems. We propose further assessments to discriminate between the models, particularly in regards to establishing boundary conditions and comparing to explicit-solvent molecular dynamics simulations.

  6. Atomic disorder and superconductivity in A15 materials

    International Nuclear Information System (INIS)

    Faehnle, M.

    1982-01-01

    The validity of a modified linear chain model for describing the properties of A15 superconductors is discussed in detail. Using this simple model for the electronic density of states, we calculate the critical temperature and the Fermi level as functions of atomic disorder with concentration c within the framework of the BCS theory. Thereby the experimentally observed saturation effect of the critical temperature is reproduced by taking into account the contribution of three-dimensional electronic states. The microscopic versions of the Ginzburg-Landau equations for systems with a strongly varying electronic density of states and a strongly varying electron velocity are derived for clean and dirty superconductors in order to calculate the Ginzburg-Landau parameter, the coherence length, the penetration depth, and the upper critical field as functions of atomic disorder. It is shown that these quantities depend strongly on the values inserted for the mean free electron path 1(c). Good agreement between theoretical and experimental results is obtained by an appropriate choice of 1(c). In contrast, the thermodynamic critical field is nearly independent of 1(c). In all cases we derive a depression of the pinning forces and the critical current densities with increasing atomic disorder in good agreement with the experiments

  7. Set of difference spitting schemes for solving the Navier-Stokes incompressible equations in natural variables

    International Nuclear Information System (INIS)

    Koleshko, S.B.

    1989-01-01

    A three-parametric set of difference schemes is suggested to solve Navier-Stokes equations with the use of the relaxation form of the continuity equation. The initial equations are stated for time increments. Use is made of splitting the operator into one-dimensional forms that reduce calculations to scalar factorizations. Calculated results for steady- and unsteady-state flows in a cavity are presented

  8. ADI as a preconditioning for solving the convection-diffusion equation

    International Nuclear Information System (INIS)

    Chin, R.C.Y.; Manteuffel, T.A.; De Pillis, J.

    1984-01-01

    The authors examine a splitting of the operator obtained from a steady convection-diffusion equation with variable coefficients in which the convection term dominates. The operator is split into a dominant and subdominant parts consistent with the inherent directional property of the partial differential equation. The equations involving the dominant parts should be easily solved. The authors accelerate the convergence of this splitting or the outer iteration by a Chebyshev semi-iterative method. When the dominant part has constant coefficients, it can be easily solved using alternating direction implicit (ADI) methods. This is called the inner iteration. The optimal parameters for a stationary two-parameter ADI method are obtained when the eigenvalues become complex. This corresponds to either the horizontal or the vertical half-grid Reynolds number larger than unity. The Chebyshev semi-iterative method is used to accelerate the convergence of the inner ADI iteration. A two-fold increase in speed is obtained when the ADI iteration matrix has real eigenvalues, and the increase is less significant when the eigenvalues are complex. If either the horizontal or the vertical half-grid Reynolds number is equal to one, the spectral radius of the optimal ADI iterative matrix is zero. However, a high degree of nilpotency impairs rapid convergence. This problem is removed by introducing a more implicit iterative method called ADI/Gauss-Seidel (ADI/GS). ADI/GS resolves the nilpotency and, thus, converges more rapidly for half-grid Reynolds number near 1. Finally, these methods are compared with several well-known schemes on test problems. 23 references, 5 figures

  9. A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    Sufia Zulfa Ahmad

    2016-01-01

    Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

  10. Boundary conditions in Ginsburg-Landau theory and critical temperature of high-Tc superconductors

    International Nuclear Information System (INIS)

    Lykov, A.N.

    2008-01-01

    New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature (T c ) of high-T c superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T c of cuprate superconductors

  11. Formulae of differentiation for solving differential equations with complex-valued random coefficients

    International Nuclear Information System (INIS)

    Kim, Ki Hong; Lee, Dong Hun

    1999-01-01

    Generalizing the work of Shapiro and Loginov, we derive new formulae of differentiation useful for solving differential equations with complex-valued random coefficients. We apply the formulae to the quantum-mechanical problem of noninteracting electrons moving in a correlated random potential in one dimension

  12. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  13. Solving inverse problems for biological models using the collage method for differential equations.

    Science.gov (United States)

    Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R

    2013-07-01

    In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.

  14. Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

    Science.gov (United States)

    Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

    2018-03-01

    Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

  15. V L Ginzburg and the Atomic Project

    Science.gov (United States)

    Ritus, V. I.

    2017-04-01

    This paper is an expanded version of the author's talk presented at a session of the Physical Sciences Division of the Russian Academy of Sciences celebrating the 100th anniversary of V L Ginzburg's birth. Tamm's Special group was organized in June 1948 with the task to clarify the feasibility of constructing a hydrogen bomb. Having verified and confirmed the calculated results by Ya B Zel'dovich's group, the Tamm group proposed an original hydrogen bomb design, which, following A D Sakharov's idea, consisted of an atomic bomb surrounded spherically by nested uranium and heavy water layers: the heavy water, on V L Ginzburg's suggestion, was replaced by higher-calorie solid lithium-6 deuteride. The ionization implosion of deuterium by uranium, both heated by the atomic bomb's explosion, greatly accelerates nuclear reactions in deuterium and uranium and increases the total energy release. Upon their approval by the KB-11 top researchers, the Atomic project leadership, and the government, the proposals were implemented in the RDS-6s bomb, which was successfully tested on 12 August 1953. Lithium-6 deuteride turned out to be a convenient multipurpose nuclear fuel. The paper highlights the recognition by the leaders of the country and of the Atomic project that fundamental science plays a crucial role in promoting scientists' ideas and proposals.

  16. Solving Coupled Gross--Pitaevskii Equations on a Cluster of PlayStation 3 Computers

    Science.gov (United States)

    Edwards, Mark; Heward, Jeffrey; Clark, C. W.

    2009-05-01

    At Georgia Southern University we have constructed an 8+1--node cluster of Sony PlayStation 3 (PS3) computers with the intention of using this computing resource to solve problems related to the behavior of ultra--cold atoms in general with a particular emphasis on studying bose--bose and bose--fermi mixtures confined in optical lattices. As a first project that uses this computing resource, we have implemented a parallel solver of the coupled time--dependent, one--dimensional Gross--Pitaevskii (TDGP) equations. These equations govern the behavior of dual-- species bosonic mixtures. We chose the split--operator/FFT to solve the coupled 1D TDGP equations. The fast Fourier transform component of this solver can be readily parallelized on the PS3 cpu known as the Cell Broadband Engine (CellBE). Each CellBE chip contains a single 64--bit PowerPC Processor Element known as the PPE and eight ``Synergistic Processor Element'' identified as the SPE's. We report on this algorithm and compare its performance to a non--parallel solver as applied to modeling evaporative cooling in dual--species bosonic mixtures.

  17. Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

    Science.gov (United States)

    Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

  18. Free-complement local-Schrödinger-equation method for solving the Schrödinger equation of atoms and molecules: Basic theories and features

    Science.gov (United States)

    Nakatsuji, Hiroshi; Nakashima, Hiroyuki

    2015-02-01

    The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and HTQ methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke's atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world's most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schrödinger equation of general atoms and molecules.

  19. Gabor Wave Packet Method to Solve Plasma Wave Equations

    International Nuclear Information System (INIS)

    Pletzer, A.; Phillips, C.K.; Smithe, D.N.

    2003-01-01

    A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

  20. Pairing in the cosmic neutrino background

    International Nuclear Information System (INIS)

    Alonso, V.; Paredes, R.

    1981-07-01

    We extend the discussion of the possible superfluidity of the cosmic background of neutrinos beyond the arguments based on the gap equation, originally given by Ginzburg and Zharkov. We show how to develop a simple Ginzburg-Landau liquid model, in analogy with superconductivity. We use it to show how an analysis of the energy spectrum of the universe can be formulated to include general relativistic effects on the superfluid neutrinos. Finally, in view of the Hawking and Collins careful discussion on the rotation and distortion of a spatially homogeneous and isotropic universe, we discuss the vortex dynamics that might be generated on the superfluid by rotations (allowed by the almost isotropy of the microwave background of photons) of up to 2 x 10 -14 second of arc/century, but conclude that rotations of this order of magnitude would be sufficiently strong to deter the existence of the superfluid state. (author)

  1. On the molecular dynamics in the hurricane interactions with its environment

    Science.gov (United States)

    Meyer, Gabriel; Vitiello, Giuseppe

    2018-06-01

    By resorting to the Burgers model for hurricanes, we study the molecular motion involved in the hurricane dynamics. We show that the Lagrangian canonical formalism requires the inclusion of the environment degrees of freedom. This also allows the description of the motion of charged particles. In view of the role played by moist convection, cumulus and cloud water droplets in the hurricane dynamics, we discuss on the basis of symmetry considerations the role played by the molecular electrical dipoles and the formation of topologically non-trivial structures. The mechanism of energy storage and dissipation, the non-stationary time dependent Ginzburg-Landau equation and the vortex equation are studied. Finally, we discuss the fractal self-similarity properties of hurricanes.

  2. Theory for electric dipole superconductivity with an application for bilayer excitons.

    Science.gov (United States)

    Jiang, Qing-Dong; Bao, Zhi-qiang; Sun, Qing-Feng; Xie, X C

    2015-07-08

    Exciton superfluid is a macroscopic quantum phenomenon in which large quantities of excitons undergo the Bose-Einstein condensation. Recently, exciton superfluid has been widely studied in various bilayer systems. However, experimental measurements only provide indirect evidence for the existence of exciton superfluid. In this article, by viewing the exciton in a bilayer system as an electric dipole, we derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equations, we discover the Meissner-type effect and the electric dipole current Josephson effect. These effects can provide direct evidence for the formation of the exciton superfluid state in bilayer systems and pave new ways to drive an electric dipole current.

  3. Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach

    Science.gov (United States)

    Khotimah, Rita Pramujiyanti; Masduki

    2016-01-01

    Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

  4. Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations

    Directory of Open Access Journals (Sweden)

    Bahman Ghazanfari

    2013-08-01

    Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.

  5. Integrator Performance Analysis In Solving Stiff Differential Equation System

    International Nuclear Information System (INIS)

    B, Alhadi; Basaruddin, T.

    2001-01-01

    In this paper we discuss the four-stage index-2 singly diagonally implicit Runge-Kutta method, which is used to solve stiff ordinary differential equations (SODE). Stiff problems require a method where step size is not restricted by the method's stability. We desire SDIRK to be A-stable that has no stability restrictions when solving y'= λy with Reλ>0 and h>0, so by choosing suitable stability function we can determine appropriate constant g) to formulate SDIRK integrator to solve SODE. We select the second stage of the internal stage as embedded method to perform low order estimate for error predictor. The strategy for choosing the step size is adopted from the strategy proposed by Hall(1996:6). And the algorithm that is developed in this paper is implemented using MATLAB 5.3, which is running on Window's 95 environment. Our performance measurement's local truncation error accuracy, and efficiency were evaluated by statistical results of sum of steps, sum of calling functions, average of Newton iterations and elapsed times.As the results, our numerical experiment show that SDIRK is unconditionally stable. By using Hall's step size strategy, the method can be implemented efficiently, provided that suitable parameters are used

  6. A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations

    KAUST Repository

    Zhang, Tao; Salama, Amgad; Sun, Shuyu; Zhong, Hua

    2015-01-01

    In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

  7. A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations

    KAUST Repository

    Zhang, Tao

    2015-06-01

    In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.

  8. Effective quadrature formula in solving linear integro-differential equations of order two

    Science.gov (United States)

    Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

    2017-08-01

    In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

  9. Landau levels and magneto-transport property of monolayer phosphorene

    Science.gov (United States)

    Zhou, X. Y.; Zhang, R.; Sun, J. P.; Zou, Y. L.; Zhang, D.; Lou, W. K.; Cheng, F.; Zhou, G. H.; Zhai, F.; Chang, Kai

    2015-01-01

    We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective k·p Hamiltonian and tight-binding (TB) model. At low field regime, we find that the LLs linearly depend both on the LL index n and magnetic field B, which is similar with that of conventional semiconductor two-dimensional electron gas. The Landau splittings of conduction and valence band are different and the wavefunctions corresponding to the LLs are strongly anisotropic due to the different anisotropic effective masses. An analytical expression for the LLs in low energy regime is obtained via solving the decoupled Hamiltonian, which agrees well with the numerical calculations. At high magnetic regime, a self-similar Hofstadter butterfly (HB) spectrum is obtained by using the TB model. The HB spectrum is consistent with the LL fan calculated from the effective k·p theory in a wide regime of magnetic fields. We find the LLs of phosphorene nanoribbon depend strongly on the ribbon orientation due to the anisotropic hopping parameters. The Hall and the longitudinal conductances (resistances) clearly reveal the structure of LLs. PMID:26159856

  10. Performance of a parallel algorithm for solving the neutron diffusion equation on the hypercube

    International Nuclear Information System (INIS)

    Kirk, B.L.; Azmy, Y.Y.

    1989-01-01

    The one-group, steady state neutron diffusion equation in two- dimensional Cartesian geometry is solved using the nodal method technique. By decoupling sets of equations representing the neutron current continuity along the length of rows and columns of computational cells a new iterative algorithm is derived that is more suitable to solving large practical problems. This algorithm is highly parallelizable and is implemented on the Intel iPSC/2 hypercube in three versions which differ essentially in the total size of communicated data. Even though speedup was achieved, the efficiency is very low when many processors are used leading to the conclusion that the hypercube is not as well suited for this algorithm as shared memory machines. 10 refs., 1 fig., 3 tabs

  11. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation

    Science.gov (United States)

    Jerke, Jonathan; Tymczak, C. J.; Poirier, Bill

    We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schrödinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation.

  12. A Proposed Method for Solving Fuzzy System of Linear Equations

    Directory of Open Access Journals (Sweden)

    Reza Kargar

    2014-01-01

    Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

  13. The infrared behaviour of the running coupling in Landau gauge QCD

    International Nuclear Information System (INIS)

    Alkofer, R.; Fischer, C.S.; Smekal, L. von.

    2002-01-01

    Approximate solutions for the gluon and ghost propagators as well as the running coupling in Landau gauge Yang-Mills theories are presented. These propagators obtained from the corresponding Dyson-Schwinger equations are in remarkable agreement with those of recent lattice calculations. The resulting running coupling possesses an infrared fixed point, α s (0) = 8.92/N for all gauge SU(N). Above one GeV the running coupling rapidly approaches its perturbative form (Authors)

  14. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  15. Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

    Science.gov (United States)

    Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

    2016-11-01

    In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

  16. New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Hassan Kamil Jassim

    2015-01-01

    Full Text Available We discuss new approaches to handling Fokker Planck equation on Cantor sets within local fractional operators by using the local fractional Laplace decomposition and Laplace variational iteration methods based on the local fractional calculus. The new approaches maintain the efficiency and accuracy of the analytical methods for solving local fractional differential equations. Illustrative examples are given to show the accuracy and reliable results.

  17. Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

    KAUST Repository

    Cortes, Adriano Mauricio; Vignal, Philippe; Sarmiento, Adel; Garcí a, Daniel O.; Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

    2014-01-01

    In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

  18. Physics of Limiting Phenomena in Superconducting Microwave Resonators: Vortex Dissipation, Ultimate Quench and Quality Factor Degradation Mechanisms

    Energy Technology Data Exchange (ETDEWEB)

    Checchin, Mattia [Illinois Inst. of Technology, Chicago, IL (United States)

    2016-12-01

    superheating field, which is intimately correlated to the penetration of magnetic flux vortices in the material. Experimental data for N-doped cavities suggest that uniform Ginzburg-Landau parameter cavities are statistically limited by the lower critical field, in terms of accelerating gradient. By introducing a Ginzburg-Landau parameter profile at the cavity rf surface--dirty layer--the accelerating gradient of superconducting resonators can be enhanced. The description of the physics behind the accelerating gradient enhancement as a consequence of the dirty layer is carried out by solving numerically the Ginzburg-Landau equations for the layered system. The enhancement is showed to be promoted by the higher energy barrier to vortex penetration, and by the enhanced lower critical field. Another serious threat to the quality factor during the cavity operation is the extra dissipation introduced by the quench. Such quality factor degradation mechanism due to the quench, is generated by the trapping of external magnetic flux at quench spot. The purely extrinsic origin of such extra dissipation is proven by the impossibility of decrease the quality factor by quenching in a magnetic field-free environment. Also, a clear relation of the dissipation introduced by quenching to the orientation of the applied magnetic field is observed. The full recover of the quality factor by re-quenching in compensated field is possible when the trapped flux at the quench spot is modest. On the contrary, when the trapped magnetic flux is too large, the quality factor degradation may become irreversible by this technique, likely due to the outward flux migration beyond the normal zone opening during the quench.

  19. Physics of limiting phenomena in superconducting microwave resonators: Vortex dissipation, ultimate quench and quality factor degradation mechanisms

    Science.gov (United States)

    Checchin, Mattia

    field, which is intimately correlated to the penetration of magnetic flux vortices in the material. Experimental data for N-doped cavities suggest that uniform Ginzburg-Landau parameter cavities are statistically limited by the lower critical field, in terms of accelerating gradient. By introducing a Ginzburg-Landau parameter profile at the cavity rf surface--dirty layer--the accelerating gradient of superconducting resonators can be enhanced. The description of the physics behind the accelerating gradient enhancement as a consequence of the dirty layer is carried out by solving numerically the Ginzburg-Landau equations for the layered system. The enhancement is showed to be promoted by the higher energy barrier to vortex penetration, and by the enhanced lower critical field. Another serious threat to the quality factor during the cavity operation is the extra dissipation introduced by the quench. Such quality factor degradation mechanism due to the quench, is generated by the trapping of external magnetic flux at the quench spot. The purely extrinsic origin of such extra dissipation is proven by the impossibility of decrease the quality factor by quenching in a magnetic field-free environment. Also, a clear relation of the dissipation introduced by quenching to the orientation of the applied magnetic field is observed. The full recover of the quality factor by re-quenching in compensated field is possible when the trapped flux at the quench spot is modest. On the contrary, when the trapped magnetic flux is too large, the quality factor degradation may become irreversible by this technique, likely due to the outward flux migration beyond the normal zone opening during the quench.

  20. Solving the Einstein constraint equations on multi-block triangulations using finite element methods

    Energy Technology Data Exchange (ETDEWEB)

    Korobkin, Oleg; Pazos, Enrique [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Aksoylu, Burak [Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 (United States); Holst, Michael [Department of Mathematics, University of California at San Diego 9500 Gilman Drive La Jolla, CA 92093-0112 (United States); Tiglio, Manuel [Department of Physics, University of Maryland, College Park, MD 20742 (United States)

    2009-07-21

    In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor psi. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

  1. Solving the Einstein constraint equations on multi-block triangulations using finite element methods

    International Nuclear Information System (INIS)

    Korobkin, Oleg; Pazos, Enrique; Aksoylu, Burak; Holst, Michael; Tiglio, Manuel

    2009-01-01

    In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor ψ. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

  2. Structure of vortices in superfluid 3He A-like phase in uniaxially stretched aerogel

    International Nuclear Information System (INIS)

    Aoyama, Kazushi; Ikeda, Ryusuke

    2009-01-01

    Possible vortex-core transitions in A-like phase of superfluid 3 He in uniaxially stretched aerogel are investigated. Since the global anisotropy in this system induces the polar pairing state in a narrow range close to the superfluid transition in addition to the A-like and B-like phases, the polar state may occur in the core of a vortex in the A-like phase identified with the ABM pairing state, like in the case of the bulk B phase where a core including the ABM state is realized at higher pressures. We examine the core structure of a single vortex under the boundary condition compatible with the Mermin-Ho vortex in the presence of the dipole interaction. Following Salomaa and Volovik's approach, we numerically solve the Ginzburg-Landau equation for an axially symmetric vortex and, by examining its stability against nonaxisymmetric perturbations, discuss possible vortex core states. It is found that a first order transition on core states may occur on warming from an axisymmetric vortex with a nonunitary core to a singular vortex with the polar core.

  3. Structure of vortices in superfluid 3He A-like phase in uniaxially stretched aerogel

    Science.gov (United States)

    Aoyama, Kazushi; Ikeda, Ryusuke

    2009-02-01

    Possible vortex-core transitions in A-like phase of superfluid 3He in uniaxially stretched aerogel are investigated. Since the global anisotropy in this system induces the polar pairing state in a narrow range close to the superfluid transition in addition to the A-like and B-like phases, the polar state may occur in the core of a vortex in the A-like phase identified with the ABM pairing state, like in the case of the bulk B phase where a core including the ABM state is realized at higher pressures. We examine the core structure of a single vortex under the boundary condition compatible with the Mermin-Ho vortex in the presence of the dipole interaction. Following Salomaa and Volovik's approach, we numerically solve the Ginzburg-Landau equation for an axially symmetric vortex and, by examining its stability against nonaxisymmetric perturbations, discuss possible vortex core states. It is found that a first order transition on core states may occur on warming from an axisymmetric vortex with a nonunitary core to a singular vortex with the polar core.

  4. A rational function based scheme for solving advection equation

    International Nuclear Information System (INIS)

    Xiao, Feng; Yabe, Takashi.

    1995-07-01

    A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author)

  5. A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

    Science.gov (United States)

    Tayebi, A.; Shekari, Y.; Heydari, M. H.

    2017-07-01

    Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

  6. Solving large sets of coupled equations iteratively by vector processing on the CYBER 205 computer

    International Nuclear Information System (INIS)

    Tolsma, L.D.

    1985-01-01

    The set of coupled linear second-order differential equations which has to be solved for the quantum-mechanical description of inelastic scattering of atomic and nuclear particles can be rewritten as an equivalent set of coupled integral equations. When some type of functions is used as piecewise analytic reference solutions, the integrals that arise in this set can be evaluated analytically. The set of integral equations can be solved iteratively. For the results mentioned an inward-outward iteration scheme has been applied. A concept of vectorization of coupled-channel Fortran programs, based on this integral method, is presented for the use on the Cyber 205 computer. It turns out that, for two heavy ion nuclear scattering test cases, this vector algorithm gives an overall speed-up of about a factor of 2 to 3 compared to a highly optimized scalar algorithm for a one vector pipeline computer

  7. Performance prediction of gas turbines by solving a system of non-linear equations

    Energy Technology Data Exchange (ETDEWEB)

    Kaikko, J

    1998-09-01

    This study presents a novel method for implementing the performance prediction of gas turbines from the component models. It is based on solving the non-linear set of equations that corresponds to the process equations, and the mass and energy balances for the engine. General models have been presented for determining the steady state operation of single components. Single and multiple shad arrangements have been examined with consideration also being given to heat regeneration and intercooling. Emphasis has been placed upon axial gas turbines of an industrial scale. Applying the models requires no information of the structural dimensions of the gas turbines. On comparison with the commonly applied component matching procedures, this method incorporates several advantages. The application of the models for providing results is facilitated as less attention needs to be paid to calculation sequences and routines. Solving the set of equations is based on zeroing co-ordinate functions that are directly derived from the modelling equations. Therefore, controlling the accuracy of the results is easy. This method gives more freedom for the selection of the modelling parameters since, unlike for the matching procedures, exchanging these criteria does not itself affect the algorithms. Implicit relationships between the variables are of no significance, thus increasing the freedom for the modelling equations as well. The mathematical models developed in this thesis will provide facilities to optimise the operation of any major gas turbine configuration with respect to the desired process parameters. The computational methods used in this study may also be adapted to any other modelling problems arising in industry. (orig.) 36 refs.

  8. Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

  9. On a numereeical method for solving the Faddv integral equation without deformation of contour

    International Nuclear Information System (INIS)

    Belyaev, V.O.; Moller, K.

    1976-01-01

    A numerical method is proposed for solving the Faddeev equation for separable potentials at positive total energy. The method is based on the fact that after applying a simple interpolation procedure the logarithmic singularities in the kernel of the integral equation can be extracted in the same way as usually the pole singularity is extracted. The method has been applied to calculate the eigenvalues of the Faddeev kernel

  10. Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

    Science.gov (United States)

    Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

    2017-12-01

    We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

  11. Stochastic resonance based on modulation instability in spatiotemporal chaos.

    Science.gov (United States)

    Han, Jing; Liu, Hongjun; Huang, Nan; Wang, Zhaolu

    2017-04-03

    A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.

  12. (2,2) superconformal bootstrap in two dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Ying-Hsuan [Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Shao, Shu-Heng [Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138 (United States); School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States); Wang, Yifan [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Yin, Xi [Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138 (United States)

    2017-05-19

    We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories numerically with semidefinite programming. We constrain gaps in the non-BPS spectrum through the operator product expansion of BPS operators, in ways that depend on the moduli of exactly marginal deformations through chiral ring coefficients. In some cases, our bounds on the spectral gaps are observed to be saturated by free theories, by N=2 Liouville theory, and by certain Landau-Ginzburg models.

  13. Pattern control and suppression of spatiotemporal chaos using geometrical resonance

    International Nuclear Information System (INIS)

    Gonzalez, J.A.; Bellorin, A.; Reyes, L.I.; Vasquez, C.; Guerrero, L.E.

    2004-01-01

    We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schroedinger, phi (cursive,open) Greek 4 , and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743

  14. Interacting loop-current model of superconducting networks

    International Nuclear Information System (INIS)

    Chi, C.C.; Santhanam, P.; Bloechl, P.E.

    1992-01-01

    The authors review their recent approximation scheme to calculate the normal-superconducting phase boundary, T c (H), of a superconducting wire network in a magnetic field in terms of interacting loop currents. The theory is based on the London approximation of the linearized Ginzburg-Landau equation. An approximate general formula is derived for any two-dimensional space-filling lattice comprising tiles of two shapes. Many examples are provided illustrating the use of this method, with a particular emphasis on the fluxoid distribution. In addition to periodic lattices, quasiperiodic lattices and fractal Sierpinski gaskets are also discussed

  15. Who Solved the Bernoulli Differential Equation and How Did They Do It?

    Science.gov (United States)

    Parker, Adam E.

    2013-01-01

    The Bernoulli brothers, Jacob and Johann, and Leibniz: Any of these might have been first to solve what is called the Bernoulli differential equation. We explore their ideas and the chronology of their work, finding out, among other things, that variation of parameters was used in 1697, 78 years before 1775, when Lagrange introduced it in general.

  16. Solving the RPA eigenvalue equation in real-space

    CERN Document Server

    Muta, A; Hashimoto, Y; Yabana, K

    2002-01-01

    We present a computational method to solve the RPA eigenvalue equation employing a uniform grid representation in three-dimensional Cartesian coordinates. The conjugate gradient method is used for this purpose as an interactive method for a generalized eigenvalue problem. No construction of unoccupied orbitals is required in the procedure. We expect this method to be useful for systems lacking spatial symmetry to calculate accurate eigenvalues and transition matrix elements of a few low-lying excitations. Some applications are presented to demonstrate the feasibility of the method, considering the simplified mean-field model as an example of a nuclear physics system and the electronic excitations in molecules with time-dependent density functional theory as an example of an electronic system. (author)

  17. Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation

    Science.gov (United States)

    Laslier, Benoît; Toninelli, Fabio Lucio

    2018-03-01

    We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the {L× L} torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167-192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2 n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat equation (Wilson in Ann Appl Probab 14:274-325, 2004). In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as L\\to∞ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C 2 differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincaré Theor Math Phys 18:2007-2043, 2017) on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg-Landau model (Funaki and Spohn in Commun Math Phys 85:1-36, 1997; Nishikawa in Commun Math Phys 127:205-227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.

  18. Study of the heavy ions (Au+Au at 150 AMeV) collisions with the FOPI detector. Comparison with the Landau-Vlasov model; Etude des collisions d`ions lourds AU+AU a 150 A.MeV avec le detecteur FOPI. Comparaison avec le modele de Landau-Vlasov

    Energy Technology Data Exchange (ETDEWEB)

    Boussange, S

    1995-09-15

    In this thesis, heavy ions (Au+Au) collisions experiments are made at 150 AMeV.In the first part, a general study of the nuclear matter equation is presented. Then the used Landau-Vlasov theoretical model is describe. The third part presents the FOPI experience and the details of how to obtain this theoretical predictions (filter, cuts, corrections, possible centrality selections).At the end, experimental results and comparisons with the Landau-Vlasov model are presented. (TEC). 105 refs., 96 figs., 14 tabs.

  19. A Regularized Approach for Solving Magnetic Differential Equations and a Revised Iterative Equilibrium Algorithm

    International Nuclear Information System (INIS)

    Hudson, S.R.

    2010-01-01

    A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria.

  20. Solving delay differential equations in S-ADAPT by method of steps.

    Science.gov (United States)

    Bauer, Robert J; Mo, Gary; Krzyzanski, Wojciech

    2013-09-01

    S-ADAPT is a version of the ADAPT program that contains additional simulation and optimization abilities such as parametric population analysis. S-ADAPT utilizes LSODA to solve ordinary differential equations (ODEs), an algorithm designed for large dimension non-stiff and stiff problems. However, S-ADAPT does not have a solver for delay differential equations (DDEs). Our objective was to implement in S-ADAPT a DDE solver using the methods of steps. The method of steps allows one to solve virtually any DDE system by transforming it to an ODE system. The solver was validated for scalar linear DDEs with one delay and bolus and infusion inputs for which explicit analytic solutions were derived. Solutions of nonlinear DDE problems coded in S-ADAPT were validated by comparing them with ones obtained by the MATLAB DDE solver dde23. The estimation of parameters was tested on the MATLB simulated population pharmacodynamics data. The comparison of S-ADAPT generated solutions for DDE problems with the explicit solutions as well as MATLAB produced solutions which agreed to at least 7 significant digits. The population parameter estimates from using importance sampling expectation-maximization in S-ADAPT agreed with ones used to generate the data. Published by Elsevier Ireland Ltd.